It's a self-piercing saddle valve like this one: https://www.youtube.com/watch?v=FB76LXrYKsU . If you're familiar with electronics, it works a lot like the so-called "vampire tap" for coax cable.
Regardless, it's a quick and easy solution in the short-term, but they tend not to last. Because they are cheap, they tend to fail easily, and because they are easy, they tend to be used in situations where they aren't really appropriate.
If this valve is actually supplying water to something, it'd be worth replacing this valve with a true T-connection and a "real" valve.
If it's NOT supplying water to something, it'd be a good idea to remove it and patch the gap with a proper coupling.
There's also the possibility that you could remove it and just patch the hole that it leaves behind, but that might not last very long either.
If you're up for it, soldering copper pipe is not at all beyond the adventurous homeowner, but it is a pretty advanced task, so you're not going to find a kit or instructions at Lowe's. You'll have to learn about soldering (a non-trivial task), and get the proper equipment (a propane torch, flux, and solder).
I just spent two years adding insulation and replacing the siding on my house by myself, and if I was in your shoes, I'd hire a plumber ;-)
Hope that helps!