Titans are humans. The reason the weak spot is around the neck is because once that area is sliced the 'human' is killed and the titan body can no longer regenerate.
As to how people unlock that power? Nobody knows. People think Eren obtained it by being injected by something his father gave him, but currently that looks incorrect. It is likely that injection was actually the ability to control titans. This is the reason Bert/Reiner/Annie were after him.
Monkey Trouble (a big monkey titan that later appears) seems to have the ability to make humans turn into titans on will. He does this to an entire village, including Connie's mom. As to how he does that, we have no idea.