Dictionary Definition:

“[The conjugate base is] related to the corresponding acid by the loss of a proton.”

Selected from OxfordDictionaries.com

Functional Definition: 

In a reaction the conjugate base is the molecule that is formed once the acid looses its proton. The conjugate base is usually charged.

This is the same image you saw for the conjugate acid definition. This time notice how the conjugate base has one less proton. In this example NH4+ is a strong acid and its conjugate base NH3 is a weak base.

Figure courtesy of Schlenk of Wikipedia Commons