To be communicative is to have the ability to communicate — to exchange thoughts and ideas. Couples often go to counseling to learn to be more communicative.
It's easy to see the verb communicate in the adjective communicative: a communicative person is one who can communicate easily. Being communicative is one of the qualities we most value in other people. There's nothing more frustrating than a person who's not communicative, because you can't talk to them. I'm surprised when others are surprised at how communicative my dog is. Aren't all dogs good at talking to their owners?