When you cut them apart, both parts will continue to live. Under the microscope you can even see that the head will grow a remaining body over the course of several days.
The name of the worm is Aeolosoma, and it is a common fresh-water worm. It is about 3-5mm in length and it reproduces mostly asexually. When a worm is large enough it will split to form two worms. When cutting the worm apart, we can see that the head continues to move just like before and that it will grow.