(1) To use ambiguous language, especially in order to deceive. (2) To avoid giving a direct answer.
Example:
As the company directors continued to equivocate, the union prepared to return to the picket lines.
Equivocate contains the root equi, meaning "equal." It thus suggests that whatever is said has two equally possible meanings. The person who equivocates avoids giving a clear, unequivocal message. Politicians are often said to equivocate, but equivocating is also typical of used-car salesmen or nervous witnesses in a courtroom. Sometimes even husbands and wives will equivocate to avoid a quarrel.