The Seven Years' War helped pave the way for the colonies' break with Britain in several ways. This answer will focus on three.
First, the conduct of the Seven Years' War, which ended as a staggering victory on a global scale for Great Britain, nevertheless placed a heavy financial burden on the Crown. In order to meet that burden, a series of royal ministers attempted a broad restructuring of the nation's finances. One aspect of this new approach to financing the national debt was imposing new taxes on Britain's American colonies. Taxes like the Stamp Act and others did not sit well with colonial assemblies, who argued that only they possessed the authority to impose internal taxes. Moreover, even enforcement of older trade regulations was intensified, a development that angered colonial merchants accustomed to what one British parliament member famously called "salutary neglect." In short, the expense of the war led to a constitutional crisis in which the colonies asserted their rights, as British subjects, not to be taxed without their consent.
Second, the French and Indian War, as the American iteration of the Seven Years' War, resulted in British control of all lands east of the Mississippi River. This development was eagerly anticipated by Americans, especially influential land speculators who had bought up lands in the Ohio Valley and the settlers who hoped to move there. Indian peoples who had survived for more than a century by "playing off" British and French interests, now faced inexorable British American expansion. Pontiac's Rebellion, which inflamed the Ohio Valley and the Old Northwest in the wake of the French and Indian War, was in part a consequence of this new reality. The Crown, in the meantime, instituted the Proclamation of 1763, which banned American settlement west of the Appalachians. This angered American speculators, especially in Virginia. It also necessitated the presence of British soldiers, an affront to American sensibilities as well as an additional cost to be underwritten by taxation.
Finally, the French and Indian War helped to upset a longstanding affinity between the colonials and the British. British officers were especially unimpressed by colonial militia. For their part, militiamen were horrified by the brutal discipline and offended by the arrogance of British military leaders. Many in Parliament and the military leadership were angered at the unwillingness of colonial assemblies to vote for taxes to finance the war effort or to raise militia forces (indeed, this was one reason Parliament sought to "take the bull by the horns" with the Stamp Act in 1765.)
Overall, the Seven Years' War caused (and was in many ways a part of) British attempts to consolidate their power, financial and otherwise, over their empire. This paved the way for a colonial break with Britain.