To "expand your horizons" means to gain experiences, and to learn about different cultures and ways of living. People often use this phrase to talk about visiting other countries, getting new jobs, or getting more education. "Expanding your horizons" sounds very positive and optimistic.
This phrase uses the word "horizon", which is the line where the ground and the sky seem to touch each other. So you can imagine that "expanding" your horizon means that the area you are able to see becomes larger.