Hi,

I am an English for Sciences (ESP) teacher and the above answers are correct. I am adding the following though:

In easy English: It is a rock under the ground that can absorb and hold water. 

In more difficult, but more scientific English: An aquifer is an underground layer of water-bearing rock. These water-bearing rocks are permeable rocks. This means that there are small openings (microscopic/very small) inside the rock where liquids and gasses can pass through.This means that the water from the topsoil drains through the ground and gets collected in an aquifer. The water from an aquifer can either be drinkable or unsuitable for drinking. You normally have to drill down into an acquifer to get to the water. 

Extra vocab: water-bearing rock - a rock that holds water for example an underground cavern.
Extra vocab: permeable - usually a kind of material (like a rock or a membrane) that allows for liquids or gasses to pass through it.

Good luck with your vocab!