A good question!
If you have begun or ended a line of machine stitching in the middle of your quilt, you have to deal with the two thread ends. Some people backstitch to secure the threads, or perhaps use very tiny stitches as they get to the end of the line, then cut the thread ends off right there.
But I have seen too many such finishes that don't look finished at all. The scissors can't reach exactly to the surface of the quilt, so the thread ends stick up in little eyelashes. Or the backstitch didn't really secure the threads, so over time the quilting comes unsewed. I think it's much more professional to pull both ends to either the front or back of the quilt, tie them, thread them into a needle and make the threads disappear between the layers of the quilt.
This is time-consuming, of course, even if your eyes are good enough to thread a needle without difficulty (mine aren't). I have used self-threading needles but they tend to shred rayon or shiny polyester thread. It's much easier to just use a needle threader.
I should give a shout-out to Robbi Joy Eklow, another Quiltart list maven, who champions an alternative method of sinking thread ends. It really works, and I have used it on occasion but not enough to really get into the rhythm and internalize the method. I'll show you how it works (wish I could send you to Robbi's website, but I can't find this anywhere publicly posted) but as for me, I'm just so happy with all the needle threaders that Katy sent me last year, I'll probably stick with my own method forever.
In either case, here's the tutorial:
My method -- with needle threader