Dictionary Definition: 

“A compound or ionic species that can accept an electron pair from a donor compound.”

Selected from OxfordDictionaries.com

Functional Definition:

The problem with the Brønsted-Lowry acid definition is that it limits what we can consider acids. To broaden how we define acids we call any molecule that can take on an electron pair from another molecule a Lewis Acid.  This means that a molecule does not need to have a proton to be an acid.

In the figure bellow the red boxed molecules are Lewis acids, they are accepting electrons from  the attacking or arrow-pointing molecules.

Figure courtesy of Myceteae of Wikipedia Commons