Specifically on the political, social and economic effects.
Reaching back into my first year history course; within Ireland specifically both set off a chain of events which would lead to a widespread rebellion which lingered long in folk memory but largely failed in its immediate objectives. Ireland had, since the War of the Two Kings 1689-91 (a theatre of the Nine Years' War and the military struggle resultant from the Glorious Revolution of 1688/89), been divided between a Protestant (Anglican) Anglo-Irish ascendancy who formed the elite of society, and the Catholic and Dissenting (Methodist, Presbyterian, etc.) masses who formed the rest of society. The Dissenters were largely descended from the Ulster Scots and English settlers who had come over during the Ulster Plantations of the early 1600s and the Cromwellian Settlement of the 1650s, whereas the Catholic community was primarily composed of the Gaelic Irish and the Old English who had settled in Ireland during the middle ages.
Having lost the Confederate Wars of 1641-1653 and the War of the Two Kings, the Catholic element of society - the greater bulk of Irish society at that - had come to identify as being the true Irish, bound by a shared history and by common faith despite different ethnic origins. The Penal Laws imposed on the Catholic Irish as a result of their defeat in the War of the Two Kings - which forbade Catholics from holding a mortgage, from buying land and forced subdivision of inherited lands; except where an heir was Protestant, in which case they inherited it all - and the confiscation of lands following previous plantations left the Catholic population in control of only 15% of the land of Ireland by 1703 (Kee, p.19) and 5% by 1778 (Elliott, p.7). These Penal Laws forced Catholics to pay tithes to the Anglican Church of Ireland and effectively excluded Catholics from the political system too, out of an extreme distrust which had pervaded Anglo-Irish relations since Elizabeth's reign (and in Protestant eyes been proven correct by the multitude of insurrections between the end of her reign and the defeat of James II).
Jonathan Swift's satirical Modest Proposal (1720) summarises the condition of the population:
Some persons of a desponding spirit are in great concern about that vast number of poor people, who are aged, diseased, or maimed, and I have been desired to employ my thoughts what course may be taken to ease the nation of so grievous an encumbrance. But I am not in the least pain upon that matter, because it is very well known that they are every day dying and rotting by cold and famine, and filth and vermin, as fast as can be reasonably expected. And as to the young laborers, they are now in as hopeful a condition; they cannot get work, and consequently pine away for want of nourishment, to a degree that if at any time they are accidentally hired to common labor, they have not strength to perform it; and thus the country and themselves are happily delivered from the evils to come.
Throughout the mid-18th century the tensions between Catholics and Protestant simmered relatively quietly, with instances of agrarian violence targeted against the Protestant establishment, with bands of men in blackface and white shirts mutilating the cattle of landlords, and by 1760 a large scale agrarian revolt, the Whiteboy movement, saw bands of men numbering up to the hundreds tearing down land enclosures. Despite this there was no large, popular uprising against the Crown or the Irish parliament dominated by the Anglo-Irish, and interrogated Whiteboys showed 'no marks of disaffection to His Majesty's person or government' (Kee, pp. 24-26). Tensions were not at this point politicised, in part possibly because of the Irish tradition of men emigrating for military service; the Penal Laws prevented Irish Catholics from joining the Crown forces and part of the Cromwellian Settlement had been that soldiers of the Irish Catholic Confederation were deported into foreign service, exiled. A number of Irish regiments featured in the French and Spanish armies, some headed by veterans of the War of the Two Kings. Indeed, 'England permitted France to recruit openly for her Irish regiments in Ireland' throughout the early 1700s, with the Anglo-Irish firmly intent on keeping Ireland itself secure and stable (Elliott, p.7) despite these recruits becoming part of a military tradition in part devoted to the restoration of the House of Stuart.
Into this climate then add the American Revolution. Opinion in Britain and Ireland was heavily divided, with a popular view being that the Revolution was a 'fratricidal war' precipitated by British economic and political policy. In Ireland, the primarily Dissenting Ulster Scots were particularly favourable to the Revolution, having many familiar connections due to the intense migration from Ulster to the Colonies (the Ulster Scots being the progenitors of the so-called Scots-Irish) during the 1770s and beyond. For them, the revolutionaries were their kin fighting a readily-recognisable struggle against outside intervention in their own affairs. As one petition sent by Dubliners to the king detailed: British forces were engaged in 'an unnatural conflict with Protestant subjects f the same empire' (McDowell, pp.213-214).
With British defeat at Saratoga in 1778, Ireland was completely stripped of its resident armed forces and the Protestant population were forced to reconsider their own security, at risk from both the Irish Catholics and the threat of invasion from France. Also partly inspired by the success of the Americans in resisting Britain through force of arms (McDowell p.216), Ulster Protestants formed the 'Irish Volunteers', a sort of home-guard militia armed and supplied by wealthy landowners and also completely outside government control. They were also inspired by the American revolutionary struggle, taken with a sense of confident liberalism, and ended up taking a stand against what the Anglo-Irish saw as ongoing British political interference in their own affairs, where the supremacy of Westminster over the Irish parliament and the mercantilism of Britain frustrated their sense of economic and political independence from Britain. The whole ethos of the Volunteers developed a Whiggish twist of Roman republicanism, with debating clubs and grand parades of Volunteers increasingly devoted to a patriotic notion of a truly independent Irish parliament.
At this point Ireland and Great Britain were still formally independent kingdoms, and the Anglo-Irish were worried that union would be to their disadvantage. Mirroring in part the early experiences of the American revolution, the Volunteers became enmeshed in the political reform movement growing in Ireland, their colonels also political men deeply inspired by Enlightenment ideals, and they put forward a programme of reform in 1782 which challenged the pre-eminence and veto of Westminster, the corruption of the Irish parliament, an extension of the franchise to lease-holders, and the unfavourable tariffs imposed on Irish goods. However, a briefly considered proposal to extend the franchise to wealthy, landowning Catholics proved divisive and was dropped (Elliott, pp.10-14). What did transpire was that representatives from 173 Volunteer corps agreed upon a number of resolutions including:
denouncing the claim of Westminster to legislate for Ireland
denouncing British power under Poynings' Law of 1495 (which essentially required the king's privy council to approve any motions to be tabled in the Irish parliament)
demanding free trade
expressing 'pleasure' in the 1778 relaxation of a number of Penal Laws, which allowed Catholics to once again inherit land and hold leases equitable with Protestants
In the event, further relaxing of the Penal Laws occurred (including the infamous restriction on Catholics owning a horse worth more than £5), and Poynings' Law was revoked. This was a major coup for the Volunteers, though McDowell suggests that opinion had long been against the very things that they denounced and the British were only too happy to give their assent to any temporary measures which might prevent an escalation of the situation, giving rise to another colonial revolt (p. 230). In any case the sense was that the 1782 'Constitution' gave the Irish parliament the independence that it desired, and bourgeois Protestant opinion had turned towards seeing Catholics as potential allies.
Elliott, Marianne (1982) Partners in Revolution: The United Irishmen and France, Yale University Press.
Kee, Robert (1972) The Green Flag: A History of Irish Nationalism, Penguin.
McDowell, RB, 'Colonial Nationalism and the Winning of Parliamentary Independence 1760-82' and 'The Age of the United Irishmen: Reform and Reaction, 1789-94' in Moody, Martin, and Bryne (1986) A New History of Ireland, Volume IV: Eighteenth-Century Ireland 1691-1800, Oxford University Press.