A thread tail is the portion of your beading thread that you do not use for stitching beads, at least initially.
When you prepare a beading needle and thread for single-strand beadwork, you pass the thread through the eye of the needle, pull about six to eight inches of thread through the needle, and fold that thread over on the other side. Those six to eight inches are the thread tail. You hold the thread tail and the rest of the thread (called the "working thread") against the needle while you work, to keep the needle from falling off.
"Thread tail" can also refer to the length of thread between the end of the thread and the stop bead. This tail protrudes from the beadwork until you're ready to go back and weave it in, or (if it's a long tail) use it to stitch more beadwork in the opposite direction.
