What is an Andgate?

An Andgate or more correctly an AND gate is a digital logic gate that implements logical conjunction.  Output results only if both inputs to the AND gate are present .  If neither or only one input is present, no output results.

Wikipedia can provide more information if required.

Why Andgate for the name of a business?

The description above provides a good business model because two people or two groups working together can often achieve success where one alone will fail.