When submitting mail by using sendmail as a mail submission program, sendmail copies all messages to "/var/spool/clientmqueue" first. Sendmail is a setgid smmsp program and thus gives any user the permission to do so (/var/spool/clientmqueue belongs to user and group smmsp). Later, another sendmail process, the sendmail mail transfer agent (MTA) copies the messages from /var/spool/clientmqueue to /var/spool/mqueue and sends them to their destination.
/var/spool/clientmqueue is thus the holding area used by the MSP (Mail Submission Protocol) sendmail instance before it injects the messages into the main MTA (Mail Transport Agent) sendmail instance.
Sendmail will save the message in /var/spool/clientmqueue for safe keeping before trying to connect to the MTA to get the message delivered. Normally there would be a 'queue runner' MSP sendmail instance which every half hour would retry sending any message that couldn't be sent immediately. Each message will generate a 'df' (message routing info) and 'qf' (message headers and body) file. You can list out all of the messages and their status by:
# mailq -v -Ac
When files accumulate in /var/spool/clientmqueue, this is probably due to sendmail localhost MTA not running, and thus the mails don't get send.