When it comes to Let's Plays, the reason I watch them are many:
1) Sometimes just to see if it's a game I might like
2) Sometimes to learn how a game or Mod works. Especially in Minecraft, some of the Mods are quite complex, so getting a feel for their mechanics and necessary steps helps a lot. EU IV is a very complex game which watching others play helps a lot.
3) Often it's to watch a game being played I am not interested in playing or can't play because it is a console exclusive. The Telltale games are ones I am not interested in Playing, but enjoy the Story. The Last of Us I enjoyed the Story and didn't have a Playstation to play it anyway.
4) To watch someone else play a game I have played, but don't feel like playing again.
5) The person doing the Let's Play is just entertaining. Some of the most ROFL moments I have had has been watching someone do something unexpected while playing a game.
The biggest negative about Let's Plays are that every person I have watched eventually gets annoying to me over time. I start to see them miss things, repeat mistakes, do things in an awkward manner, forget or not change Key settings that would help a lot(if I see another person toss their weapon accidentally in Minecraft I'm gonna have a coronary), repeat catch phrases, pronunciation or elocution at first is interesting then becomes annoying, and sometimes they just burn out to a point where it becomes noticeable. I almost always eventually go back to watch them again, just need a break once in awhile.