Tip Ring Sleeve connectors look like a 1/4" stereo connector but they're not. This type of cable is generally used in three settings:

(1) Balanced Patchbay

(2)connecting Balanced inputs and outputs together (ie, the output of a mixer to the input of a power amp)

(3) As an Insert cable for inserting an effect into a mixingboard channel.

The main reason for the TRS connector is it's size. It is meant to replace the XLR connector but if you've ever seen the size of such a connector you'll know that the XLR takes up much more real-estate on the surface of any rack box.

The above picture shows a TRS (Tip Ring Sleeve) male connector to an XLR Female connector but the XLR Female connector could be another TRS 1/4" male plug. When both ends are the 1/4" TRS type connectors it is usually called a patch cable.

When used as an INSERT cable the TRS is used as an unbalanced (high impedance) connection between a mixingboard and outboard gear, ie. compressor or reverb etc.... The TRS connector usually follows the following format (Notice I said usually, if you are not sure then use a volt-ohm-meter and see what the TIP and the RING are connected to You can find VOMs at Radio Shack).

When the TRS cable is used in a mixingboard setting the TIP is connected to the SEND of the mixingboards channel (Connect the SEND to the compressors input).

The RING is connected to the mixingboards RETURN (connect this to the compressors output).

If you don't know what your mixingboard insert wiring is configured to then look in the manual. Some manufacturers reverse this order just to keep us guessing.