In physics, intensity can usually be understood as the strength of something like a beam of light. To figure out (i.e., compute) the exact intensity of a beam of light or a fire hose spraying water, we need to know how many units of light or water are coming to some area in some period of time. A factory might have an "intensity" of 100 cars per day delivered to the loading dock. A fire hose might have an intensity of 100 buckets of water per minute per open window of a certain size in a burning building.
Usually when talking about intensity, we are talking about the amount or energy of particles or radiation per unit area. Since each particle spreads out from the source in a sphere, the area is measured as the surface area of this sphere, or 4*pi*r^2, where r is the distance from the source to the observer.