Computational Linguistics is a subfield of Linguistics which uses computers to aid in the research process. It should not be confused with Natural Language Processing, which is in the domain of Computer Science, and in particular Artificial Intelligence.
Corpus linguistics is made significantly easier with computers.
Generally, computational linguists study linguistic phenomenon by attempting to duplicate them with a computer, so as to confirm their hypothesis. (For example, if they believe that the grammar of a given language is G, then they will implement a parser for G, and see if that parser can accept all valid sentences in the language.)
The Association for Computational Linguistics[?] definition is: