Cold Junction Compensation is used to make the reading of the thermocouple more accurate. Think about it, you have a T/C, which is a junction of dissimilar metals. Now, for local CJC, you connect your T/C Leads to screw terminals. Guess what? There are two brand new junctions of dissimilar metals, which creates new thermocouples.
The CJC is connected in exactly the same way to the same types of screw terminals (for example) so that the error voltage produced by the extra junctions can be nullified, so ONLY the actual voltage generated by your measurement junction is measured.
Remote CJC's are used sometimes if you are actually going through more than one junction from the actual T/C to the measuring device.