The ant carries the aphid to the plant and gently deposits it on a low lying leaf.
The aphid immediately goes to work, greedily sucking the plant's lifejuices out through it's mosquito like mouth. The more the aphid eats, the more excess plant sugar builds up in it's system, eventually spilling out of it's anus as a sweet, sticky substance affectionately referred to as "honeydew." This is the most delicious substance in the world to ants, and when the ant returns that night he happily laps it up, just as the aphid happily continues to produce it.
The ant will sometimes gorge himself for hours on the sweet nectar, causing his abdomen to swell to nearly twice it's normal size. When the aphid has finally sucked all the life out of a plant, causing it's leaves to turn brown and die, the ant simply moves it to a new plant. If the new plant is large enough, the ant and his extended family will deposit as many aphids as they can on it's leaves, so there is enough "honeydew" for everybody. The ant will also viciously defend the aphid against any predator that tries to make a meal of it.
This is called "aphid farming," and it's something ants do extremely well.
I never would have believed this if I hadn't seen it with my own eyes. Yes, two ants running side by side towards the base of our spinach plants, tiny live aphids clutched in their jaws.
Two ants that are no longer with us I might add.