Tedd's Glove is a glove which Tedd uses to program magic watches. Tedd never explains it, so we can only speculate about its functionality. It is certainly a different object from Tedd's Gauntlet (not only does it look different, but we have confirmed it by Dan in commentary), but it may still have similar functionality of storing magical energy - or it may be a more complicated magic device. It doesn't seem to need a connection to computer to be used, although it may simply connect wirelessly.
We first see the glove when Grace leaves to secretly meet Adrian Raven in Death Sentence 4. After that, we are supposed to first see the glove when Tedd prepares watches with cat form for Sarah. We first see it to program watches when Tedd prepares non-furry cat form.