A make one purlwise is the purl equivalent of a regular make one, and has two variations as well: make one left purlwise and make one right purlwise.
If a pattern says to "make one purlwise" or "m1pw" without indicating "left" or "right," you can choose either one (but it's probably a good idea to keep it consistent).
If you haven't already, familiarize yourself with the different styles of knitting before continuing. There are three different ways to hold your yarn when knitting and you want to make sure you're watching the right technique for you.
m1pw - make one purlwise
m1lpw - make one left purlwise
m1rpw - make one right purlwise
MAKE ONE RIGHT
MAKE ONE LEFT