As you've already discovered, it's a slur, and it means that you should play the notes that fall under it legato.
In musical notation the Italian word legato (literally meaning "tied together") indicates that musical notes are played or sung smoothly and connected. That is, in transitioning from note to note, there should be no intervening silence.
Essentially, you want one note to stop ringing the same instant that the next begins ringing. This is obviously contrasted with staccato, where notes are played sharply and stop ringing well before the next is played. Normal playing falls in between, though generally more towards the legato side.
This is just a matter of practice to get the feel and timing right. Experiment!