Melanie,

The right to terminate a contract for "convenience" means
the right to terminate the contract unilaterally, and without
cause, e.g. at the convenience of the terminating party.   A
familiar example is the termination for convenience clause
in federal government contracts with nonprofits and
educational institutions (FAR 52.249-5).

Since the other party's exercise of its right to terminate for
convenience can come out of the blue, pay attention to the
terms and conditions of the contract dealing with issues like
adequacy of the termination notice period, payment for the
cost of uncancellable obligations, payment (or settlement)
for partially-completed work, apportionment of any fee or
profit, ownership of data, etc.

Good luck!

Jim Simpson
General Counsel
Public Health Institute
2001 Addison St., Ste. 210
Berkeley, CA 94704
(510) 644-8200
xxxxxx@publichealth.org