One insight that may help non EE educated people understand what an antenna does: The simplest form of an antenna would be just a simple point emmiting electromagnetic waves. These waves would be transmitted all around that point distributed as sphere. All points of a sphere will have the same power. Now, an antenna has a different geometry than a point that helps somehow "focus" the EM waves, so their power is not distributed around the sphere uniformally but some directions get more power depending on the antenna design.<p>Now the thing to keep in mind is that an antenna is a passive device. It does amplify the signal but it does not add any power to it, it just collects the power to specific points. This may be easier to understand with a receiving antenna (which collects the signal).<p>For example, consider the satellite dish which is of course an antenna. Due to its design it should be conceptually easy to understand that the power of the transmitted field is all gathered in a very small area in the front of the dish. The largest the dish, the smaller the point where all the transmitted power is pointed, so less power would be needed to cover largest distances (and more difficult finding where the dish needs to point).