The Gregorian calendar updated the Julian calendar by further refining the leap year system. A solar year is on average about 365.25 years, so a strict 365 day calendar would "be off" by about a day very four years, which accumulates over time such that winter's starting date will drift by nearly a month each century. Even the Romans recognized that this was too much, so the Julian calendar added an extra day once every four years to improve stability.
That still isn't a perfect fix, since the average solar year is actually a little less than 365.36 days. Over millennia, the error accumulates to a few weeks. The fix was the remove 3 leap days per 400 year cycle, which is roughly a week per millennium.
In the long term this was a good fix to make, although it does appear that the reason it had become a pressing matter in Gregory's time is because Easter was gradually slipping out of the agreed upon time of year. So as a one time measure, Pope Gregory skipped ahead by ten days to retroactively counteract the error which had accumulated and return Easter to the proper time frame.
So yes, Easter was a big part of the political impetus to correct the problem, but it was a problem which already existed, and which really ought to have been addressed eventually. I suppose that skipping ten days wasn't strictly necessary apart from Easter.