The Gettier Problem essentially boils down to this: false beliefs (through the magic of deductive reasoning) can be used to justify true beliefs, which are therefore knowledge. This is bad because if the deducer had known that their original belief was false, they would not have been able to justify their new belief. In turn, this demonstrates that the concept of justification was much weaker and less intuitive than epistemologists had previously believed.
So the obvious next step was to slap a bandaid on JTB to get JTB+: knowledge is a true belief that is justified by true beliefs (or without reference to false beliefs). However, this turns out to suffer from problems when a belief is justified insufficiently but happens to be true by chance. For example:
Say you're watching a magic show and the magician puts a rabbit into his hat. Based on your true observations, you conclude "there's a rabbit in that hat". However it turned out that your eyes deceived you: it was a stuffed rabbit. But while you were making your deduction, the magician switched it for a real rabbit*, thereby making your belief true.
Your belief about the rabbit was justified and turned out to be true, but only by luck. So something's still wrong here, and I think this is just about the point in the history of epistemology where people started questioning truth and the whole JTB enterprise fell apart.
* What, you think it's a stupid trick? Well I didn't tell you the end yet, did I?!