When you talk garrulously, you're chatty and verbose, using lots of words to say what you mean. A group of kindergartners can often be found chatting garrulously to each other.
When a politician responds garrulously to an interview question, it can be hard for her audience to find the actual answer among the chatter. But someone speaking garrulously can also be friendly and welcoming, like when you're new to group and feeling a little shy. The adverb garrulously and its related adjective garrulous both come from the Latin root garrulus, "talkative," with its origin in garrire, "to chatter."