'Babble' usually means to talk without making any sense, incoherently. To 'babble out' can mean to give some secret away in a loud manner. "He babbled out when the surprise party was going to be." However, it is not used that way much and the phrase we use for such a situation is 'blurt out'. If a person keeps speaking for a long time without making any sense, we say they are babbling on.