Imagine you're building a house (let's say a small house for the sake of comparison; something you can build alone in a day; itty bitty, crummy house, but a house nonetheless). It takes a lot of energy to build a house. By the end, you'd be tired - because you put so much energy into building it.
Now let's say that house falls down. You rip out part of the structure at the bottom, and the house falls. When the house hits the ground, there will be a big boom, because the house is releasing the energy you put into it into the earth. Kinda like if you punched the ground, you'd be releasing energy into the ground (the energy it takes to punch would leave your arm and enter whatever you punched).
So, you put energy into the house to build it, and the house has stored energy while it stands (this is called potential energy, but that's not really related), and when the house falls, it releases that energy you put into it back into the environmet.
ATP is like a house. When your body has too much energy, it uses it to build a house (or whatever building analogy you want to use) - ATP. When your body needs energy, it destroys the ATP by removing a critical structure (one of the three phosphates, if I'm not mistaken), 'causing the ATP (now ADP) to release energy. Your body uses that energy that was released to do whatever it needed it for.
So it takes energy to attach the extra phosphate to ADP, then it releases energy by removing the extra phosphate from ATP.
Is that what you didn't understand?
Plants do a similar thing by converting sunlight to sugar, so that during the night, they can get energy from the sugar they built when the sun isn't out.
ATP also offers the convenience of transportation. You can't punch the air and transfer the energy to a wall a mile away, but you can build a structure, ship it a mile away, and destroy it there. ATP can travel from cell to cell till it finds one in need of energy, and thus give the energy to that cell.
Ah, biology is beautiful.
