We have an expression "the straw that broke the camel's back." That straw is "one straw too many."
We use the "one too many" idea in the context of small issues of one kind or another that accumulate. Finally, one more issue gets added and it becomes more than the entity who is dealing with the issues can handle.
So, someone who has had "one too many" has had several drinks, and has now had one drink more than he can handle and has become drunk.
With your sentence, suppose a Russian jet flies over Turkish airspace, and the Turkish feel provoked but do not retaliate. The Russians do it several more times, and the Turkish feel increasingly provoked, but still do not retaliate. Then, the Russians fly one more jet over Turkish airspace, and that is "one provocation too many," so the Turkish retaliate.
This isn't to say automatically that the provocations were all the same thing; I'm just making up a scenario that demonstrates the idea in simple terms.