Both of them are RPGs, though Skyrim is a first person RPG (you can change to 3rd person, but it's better as 1st).
Skyrim focuses on a medieval type time with swords and shields and magic and dragons and what not, and it's absolutely massive. Barbosa has played over 100 hours and he still hasn't beaten the main missions. Of course, that's sort of an anomaly as it probably only takes about 20 or so hours to complete the main missions, but that should give you a general idea of how crazy big it is. It also has the most depth of any game I've ever played with an extremely well developed history to the game that includes religion, numerous different cultures, historical events that have shaped the world, and shit like that. You'll see if you play, it's unbelievable.
Mass Effect goes in a different direction as it takes place a couple hundred years in the future. Humans discovered a cache of alien technology on Mars that has propelled us forward in technological ability, and we discover that we are far from alone in the galaxy, one shared by dozens of other races (most of which are friendly). You play as Commander Sheppard, a human that leads a team of humans and aliens alike to stop a rogue agent, Sarren. However, there's more to Sarren than meets the eye, and that sets up Mass Effect 2 and 3 (which I don't dare spoil for you).
The gameplay is wildly different from Skyrim. It's not as massive as Skyrim and, obviously, you're shooting guns and lasers at your opponents instead of arrows or swinging swords. However, the characters in Mass Effect are much more interesting and the storyline is a lot more engrossing than Skyrim's. If you liked Star Trek than you'll probably love this game as it encompasses a lot of the same morals and lessons that Star Trek had but adds a lot more action.
