[quote name='crashpanda']Would I be able to understand the story if I haven't played the other games?[/QUOTE]
Yeah, you'd be fine to start with these as your first intro to the story, it's not all that wildly complex of a history. There's a zombie pirate LeChuck, who is of course the bad guy you fight in all the games in various ways. And then there's Elaine, the main love interest. And other than that you're just a ridiculous, awkward pirate having silly but fun adventures.
Of course, I would strongly recommend playing the earlier games for their own sake! The first two in the series have been remastered and are just great.