I would like to know the industrial/economic reasons.
The Emancipation decrees of Alexander II in 1861 did not come out of nowhere. They were a part of a whole reform package known as the Great Reforms which restructured and modernized the Russian state in the aftermath of the defeat in the Crimean War. Alexander II himself was an unlikely figure to initiate Emancipation; he shared a number of political principles as his archconservative father Nicholas I and was not a young man when he succeeded his father. But Alexander II would famously defend Emancipation to a group of nobles, that "is better to abolish serfdom from above than to wait for the time when it will begin to abolish itself from below."
Alexander II's defense of Emancipation was the culmination of a near-century long process of discomfort with the institution of serfdom. The self-styled enlightened autocrats Catherine II and Alexander I were at often at pains to square their patronage of the Enlightenment in Russia with serfdom. The religious Nicholas I at times expressed fears that God would punish him for presiding over such an immoral institution. Outside the Romanov circles, there were a number of state elites and nobles who felt that serfdom was inhumane and un-European. One group of disaffected nobles and army officers known as the Decembrists saw serfdom as evidence of the incompatibility of autocracy in the aftermath of the French Revolution. The Decembrist Revolt failed in 1825, but their ideals were a sign of a growing elite disenchantment with autocracy. Russia's nascent intelligentsia would latch onto serfdom as evidence of a retrograde state at odds with the course of history.
Yet while there was discomfort with the institution of serfdom, it was only after the Crimean defeat that the Russian state could tackle it. Both Catherine II and Alexander I issued decrees to ease the burden on the serfs and Nicholas I did take steps to enforce laws preventing maltreatment of serfs. State laws in 1803 and 1847 allowed for wealthy peasants to buy their freedom from their owners. But serfdom was the "third-rail" in nineteenth-century Russian politics. Serfdom was not only an economic system for a largely agrarian country, it was also a social and political institution. The peasant mir organized the division of land and the institutions of serfdom provided the levies for the tsar's armies. Noble economic power was intertwined with serfdom and the peasant commune likewise structured various peasant families and local power. Abolishing the system meant not only attacking entrenched interests of peasantry, nobility, and the state, but also begged the question of what would appear in its place. Nicholas I outlined the dangers of abolition in a rare appearance before the Imperial Russian State Council in 1842. The Emperor acknowledged that serfdom was not a moral institution and its days were numbered, but that "to attack it at this point would be even more destructive," than abolishing the institution root and branch.
Nicholas I instead proposed to the Council that the state gradually pave the way for emancipation. But these moves were checked by not only by the aforementioned checked interest, but by domestic and political constraints. The Decmebrists and other intellectuals' attacks upon serfdom were not isolated form their wider critique of Russian autocracy, making a solution to the serf question a politically loaded one. Moreover, Nicholas I styled himself as the gendarme of post-1815 political reaction in Europe. Encouraging wide-spread reform at home was at odds with this picture of the enforcer of the Holy Alliance and the bulwark against the liberal ideas of the French Revolution. Sergey Uvarov, who was one of the guiding lights of Nicholas I's administration, contended that while serfdom was not ideal, it was one of the foundations for autocracy. Serfdom, Uvarov maintained, was so deeply entwined with the precepts of autocracy that pulling out the roots would lead to a domino effect that would destroy the Russian state. But beyond Uvarov's dire predictions, serfdom was also the basis for Russia's army. The system of peasant conscription worked quite well for serf levies and allowed Russia to field very large armies during the Napoleonic Wars. The idea of a Russian colossus was one of the Romanov's greatest chips in post-1815 diplomacy and removing serfdom meant having to radically restructure the system of military recruitment.
Yet to turn the OP's question on its head, there is the question of why should the Tsars have abolished serfdom? The system, for all its flaws, had worked quite well by the Crimean debacle. Research on Russian serfs shows that while it was not the ideal system for an agricultural economy, serfs did eat rather well and the institution was well-adapted to Russian climactic and geographic conditions. While the fear of serf rebellion was ever-present in the nineteenth century, but serf participation in the rebellions of the eighteenth century like Pugachev's was the exception rather than the rule. Even though the serfs were in human bondage, it was a form of bondage in which they often regulated on a day to day basis. The future Decembrist Ivan Yakushkin offered his serfs the option of renting his land in 1819, but his serfs refused his offer claiming that while "we are yours, but the land is ours." Although tsarist law said otherwise, many serfs perceived that they were the true owners of the land. Few serfs elected to buy their freedom and those that did were typically serfs who were somewhat apart from the larger mir and had skills that put them in a different social estate. Moral disenchantment with serfdom and pragmatic arguments against the institution did exist, but not in a vacuum and there were plenty of people in Russia, ranging from the elite to the serfs themselves, content with only modifying the system.
But the drama of abolishing this peculiar system, coupled with the simultaneous move towards emancipation in the United States, foregrounded the importance of Emancipation in Russian history. Soviet historiography stressed this as the natural evolution of Russia into capitalism from a feudal economy and both contemporary Russian and Western commentators framed Emancipation in terms of progress. But this outsized importance given to Emancipation denudes its entanglement with other aspects of the Great Reforms and the larger trajectory of the Russian state. The mechanics of serf conscription, conscripted serfs and their children were no longer part of the serf estate, meant that raising levies had to draw from a smaller pool of serfs over time. Additionally, wider post-Napoleonic military developments were stressing a more professional form of organization and the Crimean defeat underscored the need for wider reforms in the military. The equation that serfdom equaled raw military power no longer applied in the 1850s and the Russian military machine needed to move with the times. Additionally, the professionalization of both the officer corps and the imperial bureaucracy in the nineteenth century meant that the Romanovs were no longer as dependent upon noble servitors to fulfill these roles in the Russian state. Jerome Blum argued in Lord and Peasant in Russia from the Ninth to the Nineteenth Century argued that Alexander II's Emancipation was not so much a blow for human freedom as it was a capstone for the Romanov's centuries-long process to break the power and independence of the nobility by removing their last source of independent power. While Blum's argument goes a tad too far, the architects of Emancipation did see it as strengthening autocracy. Alexander II benefited greatly from a class of relatively young servitors like Nikolai Milituin who held a more liberal view of autocracy than the more reactionary Nicholas I and Uvarov. These reformers perceived defeat as a vindication of their earlier disgruntlement and a chance to implement a guarded reform of the Russian state and society.
The Great Reforms themselves were often quite compromised and cautious. The Great Reforms decided upon an expedient solution of legal emancipation, but hobbled it with a confusing patchwork of redistribution and repayment of the landowners for the land. Emancipation created only small changes land ownership for the serf-turned peasant. Few serfs could afford to make the payment for the land outright and the Russian state lacked the resources implement emancipation in a consistent manner. The peasant commune, the mir/obshchina, negotiated with the landlords and ended up owning land and parceled it out collectively, thus reifying peasant collective organization. The Great Reforms did not create a new class of freeholders and individuals, but rather a fusion of old and new methods of agrarian political and social organization. The Zemstvo, a Great Reforms' local institution for the Russian hinterland was still predicated upon the control of peasants' movements and various peasant families still controlled peasant society at the local level much as it did under serfdom. The Great Reforms were thus ill-prepared to adjust to the demands of an industrial age and a workforce that was more mobile, had greater wealth than a peasant farmer, and more educated than his ancestors. Much as the serf problem became enmeshed in other difficulties the Romanovs and their servitors faced in the Nicholavean period, the problem of industrial modernity exerted a similar sort of vexation for both Alexander III and Nicholas II.