Raw processing power. In the computer analogy, intelligence is the combination of enough processing power with software that implements the intelligence. When people compare computers to brains, they usually seem to be ignoring the software side.
This is true, but possibly not quite exactly the way you intended. “Most people” (AKA everyone I’ve talked to about this who is not a programmer or has related IT experience) will automatically associate computing power with “power”.
Humans have intellectual “power”, since their intellect allows them to build incredibly tools, like computers. If we give computers more ((computing) power ⇒ “power” ⇒ ability to affect environment, reason and build useful tools), they will “obviously become more intelligent”.
It seems to me like a standard symbol problem unfortunately much too common even among people who should know better.