"Random" things are things that:
- you don't expect
- you can't predict
- you can't explain
"Random" is used a lot in mathematics, science, computer programming, etc. to talk about events or numbers which can't be predicted.
These days, young people use the word "random" quite a lot. For example:
A: Hey, guess who called me? Jake from high school.
B: Really? That's so random!