A "spark" is a small bit of fire or electricity. For example, you can sometimes see sparks when you unplug something from an outlet. You can also make sparks by hitting a metal blade against a stone.

When you're talking about two people, the phrase "there were sparks" means that the people were romantically attracted. You especially use this to talk about when two people meet for the first time and seem to immediately be interested in each other. 

Another version of this phrase is "feel sparks" or "feel a spark":

I like him I guess, but I didn't feel any sparks.

Sometimes you meet someone, and you immediately feel a spark, you know?