Each stone on the board has a potential to help other stones. This potential is called influence. Some stones perform that job better, some do that worse.
A very simple and understandable form of help is to serve as a ladder breaker. This kind of help is long range and directional. For example, a very distant stone can decide an outcome of a ladder. Thus one often hears that stones radiate influence.
In other cases, stones support other stones by providing connections or escape routes for weak groups or cutting off escape paths for the stones of opposition.
It is very good when the influence is combined with strength (absence of weak points), forming thickness. Still better if the same stones are used properly to build territory (see don't use thickness to make territory).
Stones that are sealed in the corners have no or very little influence (shut in). Thus one of the objectives for a play in the corner is to secure an exit to the center.