Ok the first thing you need to know is how metals change shape in the first place. If the metal was a perfect crystal the force you would need to bend it would be immense. To distor atoms have to move past one another, This actually happens at imperfections in the crystal called dislocations eg;
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The dislocation is in the middle where there are just 2 atoms where there should be 3, the simplest form of disloaction is a line dislocation where the above pattern is repeated into the screen.
If you push the top line of atoms to the right with respect to the bottom one this dislocation can move
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If it moves all the way to the right the top has moved 1 atom to the right
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Repeat this millions of times and you can bend your piece of wire.
However if 2 of these dislocations running on different axes meet they can lock together and stop moving. As more and more of the dislocations lock the metal gets more difficult to deform, and gets harder. This is known as work hardening, and is why you can't bend your wire straight again, and is how you can break a spoon if you bend it back and forth too many times (it gets stiffer until it cracks).
If you heat up the metal the two crossed dislocations can jump past each other and carry on moving, making the metal more flexible again. This is called annnealing.