/var is often where processes dump a lot of data (logs, databases, etc), and subpartitioning of /var sets a cap so that when too much data is dumped there, the application crashes instead of the whole system. /var/log is often recommended to be subpartitioned separately as well, so that logging can still go on if the application data fills up and crashes.

These kinds of overruns can be intentional DOS attacks, also, so the subpartitioning is often a security recommendation. NIST 800-171 requires separate partitions for /var, /var/log, /var/log/audit, and /var/tmp