the limit of one's patience; the last straw
Used when someone can no longer endure a situation. Often appears in phrases like 我慢の限界に達する or 我慢の限界を超える.
I finally reached the limit of my patience with his irresponsible attitude.
The constant noise is the last straw.
限界 is a general word for 'limit' or 'boundary', while 我慢の限界 specifically refers to the limit of one's patience or endurance.
我慢 means 'patience' or 'endurance'. 我慢の限界 is the point where that patience runs out.
Compound of 我慢 (patience, endurance) + の (possessive particle) + 限界 (limit). The phrase literally means 'the limit of patience'.