When someone is said to be “full of hot air,” it means that he or she talks a lot about topics that he or she doesn't really understand. This slang term has its origins in the United States, and it appears to date to the late 1800s. In addition to being “full” of it, something can be referred to simply as “hot air,” a shorthand reference to the longer saying. As a general rule, when one is accused of this, it is not a compliment.
In order to understand the meaning of this phrase, you simply need to know that as air heats, it expands. This trait is exploited to do a wide variety of things, including filling hot air balloons. In the case of a hot air balloon, the air becomes lighter than the surrounding environment, allowing the balloon to float, so one could imagine someone being so full of hot air that he or she simply floats away. Or, more simply, the speech of someone like this tends to fill a space quickly, without offering much in the way of substance.
This term is used to describe exaggerations, empty talk, and obvious hyperbole. The implication is that the speaker is talking only to hear his or her own voice; filling the space with hot air, in other words. Typically, someone who is full of hot air will cheerfully discuss complicated topics without fully grasping them, which can be a subject of amusement for people who are more knowledgeable.
Politicians in particular are often accused of being full of hot air, making empty promises that they cannot, in fact, keep. Many politicians strive to counter this classic image by pointing to previous activities that they have orchestrated or participated in, attempting to prove that they do, in fact, know what they are talking about. The term may also be used more generally to describe bombastic, pushy individuals who insist on being heard at any group or gathering, whether or not their views are helpful.
It is also possible to hear a plan or idea referred to as “hot air,” in addition to hearing the term in reference to people. The term is also sometimes used to describe organizations, suggesting that the heads of the organization are not really sure of what they are doing, and that as a result, their plans or schemes will probably end up failing.