When the TRS jack is not inserted into the insert point (confusing - too many inserts!) the tip and ring connection in the socket are internally linked. When the TRS jack is inserted, the internal path is broken, and the signal path is now routed via the external effects unit.
Note that inserts are generally appropriate for effects which interrupt the signal path such as Compressors or Gates - ie the entire signal flows through the unit and then back to the point at which it left the mixer. They are not generally appropriate for effects such as Reverb where the signal is copied to another unit, modified, and then the returned signal is "blended" with the original.
On most mixers, there are various points in the signal path at which inserts can be applied - known as Insert Points. These are typically Insert Points on each input channel, after the pre-amps but before the channel EQ. There are also often Insert Points on each subgroup (group inserts) and immediately before the main outputs (main inserts). On some Mixing Desks there may be insert points on aux ouputs.