This means to communicate or deal with someone, but the word "interact" is more general than "communicate" in that it also could include time that you spend with a person (or animal) without communicating anything.

It's interesting to watch how Toby interacts with other dogs when they meet on the street.

You can even "interact with" things that are not alive:

Good architects pay attention to the ways that people interact with buildings.

In that case, "interact" means how you use and treat the buildings.

The phrase "how we interact with each other" from the example sentence at top is pretty common in essays and speeches. It means "how people deal with other people".