With M-x jabber-get-time, you can ask what time an entity (client, server or component) thinks it is, and what time zone it thinks it is in.
You can query a server about when a certain user was last seen online. Use M-x jabber-get-last-online for that.
You can also ask a client about how long a user has been idle with M-x jabber-get-idle-time. Not all clients answer such queries, e.g. jabber.el doesn't. This command can also tell the uptime of a server or component.
The first of these commands uses the old Entity Time protocol (see XEP-0090). It has been superseded by XEP-0202, but jabber.el doesn't implement the newer protocol yet. The latter two commands use the Last Activity protocol (see XEP-0012).