The simple answer is that he's just a better option than Harper right now.
The Patriots waived Harper and no team claimed him, meaning that he has a space on the practice squad if the team so chooses. Harper needed time to develop as a route runner and he'll have plenty of work on the practice squad.
Martin isn't going to be a major starter in the offense, but he offers incremental improvements over Harper in every facet of the game. If Harper is a C grade at getting separation, Martin is a C+. If Harper is a B grade as a returnman, Martin is a B+.
Martin lines up inside and outside, just like Harper. Martin flashes quick feet and quick hands, just like Harper. Harper could very well develop into a quality receiver down the road, but Patriots head coach Bill Belichick is all about the now and right now Martin is better.
This type of play makes Belichick happy. KMartin/QB understanding blitzing DB opens hot route. https://t.co/bUGn54ebyI— Rich Hill (@PP_Rich_Hill) September 17, 2015
Martin was little used in Houston and found himself swallowed up by their depth chart this offseason. The Texans have stud DeAndre Hopkins, as well as veterans Cecil Shorts III and Nate Washington. They drafted Jalen Strong at the start of the third round and Keith Mumphery in the fifth round of this past draft. Martin never really had a chance.
The Texans claimed tackle Oday Aboushi on waivers and needed to clear a roster spot. It's very likely that the Patriots offered the Texans something like a 2018 7th round pick, and maybe even made it conditional on Martin catching a certain number of passes. Whatever the cost, it's likely minuscule and Belichick helped make the back-end of the roster slightly better than it was the day before.
The Patriots offense still has three of the flexible inside-outside receivers in Julian Edelman, Danny Amendola, and now Keshawn Martin. The main takeaway should be that New England is comfortable with Aaron Dobson as the only large target on the outside.
Martin isn't acquired to be a gamechanger. In a game of inches, Martin is just here to make the team a little bit better.