Functions are computed values and cannot perform permanent environmental changes to
SQL Server (i.e., no
UPDATE statements allowed).
A function can be used inline in
SQL statements if it returns a scalar value or can be joined upon if it returns a result set.
A point worth noting from comments, which summarize the answer. Thanks to @Sean K Anderson:
Functions follow the computer-science definition in that they MUST return a value and cannot alter the data they receive as parameters
(the arguments). Functions are not allowed to change anything, must
have at least one parameter, and they must return a value. Stored
procs do not have to have a parameter, can change database objects,
and do not have to return a value.