Three main reasons, money, money, and yet more money. There were other reasons as well. Parliament controlled not only the most prosperous and most populous parts of Britain at the start of the Civil War, which meant that their war chest was far bigger than the king's (more, and more prosperous people who were able to pay taxes), but they also controlled all of the major manufacturing centres, such as Norwich, Hull and London, which also contained nearly all of the armaments manufacturers, and, near London, at Enfield, was the only large scale gunpowder factory. As it was a Royal monopoly, it was very nearly the sole source of gunpowder in Britain. They controlled very nearly all of the big cities, thus being able to tax the trade thereof, the Navy and most of Britain's merchant fleet. Thus international trade was secure, with plenty of profitable trade to tax, and also able to pretty much prevent the king's army from easily getting supplies from abroad, even which Henrietta Maria pawning the Crown Jewels!
Parliament could, therefore, afford to equip and feed, and often pay their men, whilst the king was forced to rely on promissary notes, loans and forced loans, plunder, and demanding "protection money" from towns, called "levying contributions", and whose men were often months if not years in arrears of pay.

Most of this is taken from Christopher Hill's God's Englishman: Oliver Cromwell and the English Revolution.

As Hill points out, the New Model Army was a progression of ideas that had started in the Dutch Republic 'fifty or sixty years earlier'. Essential Hill argues that the essence of the revolution in the military was partly due to its reliance on 'the free way as against the formal' or the idea that free men fighting for a cause they believed in 'could get the better of mere professionals simply by superior morale and discipline'. Cromwell had raised troops (later called Ironsides) of 'picked men, well drilled, well equipped, well horsed, well paid'. Instead of using the traditional tactics of the day, displayed with aplomb by his Royalist adversary Prince Rupert of the Rhine, which used horse as a kind of mobile infantry, Cromwell instead used his disciplined troops as a 'battering ram'.

While Rupert opted for one devastating mass charge, that would "lose cohesion in a search for plunder and destroying enemy stragglers: 'a rabble of gentility', Monck called the royalist cavalry. As Clarendon put it...whereas Cromwell's troops, if they prevailed, or thought they were beaten and presently routed, rallied again and stood in good order till they received new orders".

At Marston Moor, it was the repeated charges of Cromwell's horse that turned the battle from defeat to victory. So discipline and well drilled troops were an obvious factor in success, not just for the Ironsides, but for the New Model too. Hill goes on to state that the New Model's 'organization, commissariat and ordnance were normally far superior to those of the enemy. Their lieutenants were organization men... In addition to its better discipline and morale, the New Model Army had behind it better business methods, better supplies, better artillery.

It also should be noted that Cromwell and Sir Thomas Fairfax 'rarely engaged unless they enjoyed superiority in numbers. At Naseby this superiority was nearly two to one'.