A channel is disabled if a channel_update message has been broadcast for that channel with the disable bit set (see BOLT 7). It means that the channel still exists but cannot be used to route payments, until it has been re-enabled.
Suppose you're A, with the following setup:
A ---ab--> B --bc--> C
And node C goes down. B will publish a channel update for channel bc with the disable bit set.
There are other cases when a channel becomes disabled, for example when its balance goes below reserve...
Note that you can have multiple channels between the same nodes, and that some of them can be enabled while others are disabled (i.e. enable/disable is channel-specific, not node-specific).
To stop your node you just need to kill its process, there is no API command to do this. The JVM handles the quit signal and notifies the node to perform clean-up. For example, there is a hook to cleanly free DB locks when using Postgres.