The word klal may best be understood by its opposite, the perat, the singular thing. When singular things come together in some form of unity, they create a klal.
In the Mishna, klal is frequently used to express a general principle that brings together several individual laws. Even in such a dry legal context, however, a klal brings about a certain power that is more than just the sum of its parts.
It is well known that, by working together, people can accomplish far more than if they work apart. This is also true in the spiritual world and is presumably part of the reason a minyan is required for public Torah reading, priestly blessings, repeating the amidah, etc. An even stronger manifestation of this idea is G-d’s unwillingness to speak to Moshe for the many years the Jews who left Egypt were wandering in the desert after the sin of the spies. Moshe may well have been the greatest man to have ever lived, but he was apparently ineligible for prophecy until he represented a group G-d had reason to speak to.
Yet as powerful as the klal may be, it does not even exist without every one of its components. This is powerfully expressed by the dedication of the Mishkan: G-d brought down His presence only when the Tabernacle was finished. While this may seem obvious, it isn’t. The Talmud points in the opposite direction when it reports that His presence only gradually left the Temple during its final days.
Hence klal and perat are interdependent. The kelal gives the perat its fullest meaning, but the perat gives the klal its very existence.