Subplots are secondary storylines in novels, longer short stories, or scripts. 

A subplot can be used to show character development of secondary characters, and can be used to draw out the suspense for what is happening to the main characters. They can be used to further develop worldbuilding, and to flesh out the main plotline by expanding on history and areas the main characters do not get to see.

In The Hobbit, everything takes place around Bilbo Baggins (for the most part). There are minor excursions to the town of Dale and the Lonely Mountain before Bilbo gets there, but there are no major separate plotlines.

In the Lord of the Rings, when the Fellowship of the Ring breaks up, there are multiple plotlines -- Frodo and Sam, Merry and Pippin, and the rest of the group, who go after Merry and Pippin.

It is important to note that subplots must assist the main plotline in order to keep a novel on track. Having a subplot that has nothing to do with the main plotline will bring in a sense of disconnect and confusion.