The question of why particles have mass is one of the greatest problems in science today. But luckily, physicists have some idea.
It's called the Higgs field. The Higgs field, if it exists, permeates space. When particles interact with the Higgs field, they acquire mass. Particles that interact strongly with the Higgs field are very massive, and particles that interact weakly are less massive or have no mass at all.
One popular analogy goes like this: Imagine that the Higgs field is a room of socializing physicists. Then a particle enters the Higgs field--she's a scientist who has made an outstanding new discovery.
She tries to push to the other side of the room, but physicists gather around her to congratulate her, making it hard for her to move. It's like she acquiring mass from the field. She interacts strongly with the field.