"Computing power" means simply the ability to perform arithmetic and logical operations within a computer. Two common measures of computing power are clock speed (e.g. "2.8 GHz") and floating-point operations, known by the acronym FLOPS (e.g. "the Intel Core i9 Extreme Edition processor can perform 1000 gigaflops/second.")
A 2.8 GHz processor has twice the computing power of a 1.4 GHz. processor. A 200-gigaflop processor has twice the computing power of a 100-gigaflop processor.
Your quotation sounds as if it comes from the 1960s and 1970s. Personal computers did not exist. Computers were too expensive to give a single person an entire computer. In order to provide an interactive computing experience, computer scientists developed "time-sharing systems," in which a single computer was connected to many users, and switched rapidly back and forth between each of them. 50 users might each use 2% of the machine's computing power.