The latest in a series of distressing but regularly tolerated events that gives rise to the first obvious sign of intolerance towards the offending party, usually in the form of a drastic decision or the offer of an ultimatum. May have come from shortening the idiom/expression "the straw that breaks the camel's back", relating the distress caused by the offending party to stacking straw on the back of a camel over time until it collapses under the weight.
After a series of non-explicit infarctions, Jimmy McGill loudly disturbing his coworkers with his bagpipes is the last straw that forces Cliff Main to fire him from his law firm without cause.