Random access means you can jump straight to any address. Give the memory an address, and after the access time you have that word, whether it's next to the previous one or at the other end of the chip.
The opposite is sequential access, like a tape: to reach a spot you must wind past everything in between, so the time depends on where you are and where you're going.
"Random" here doesn't mean unpredictable. It means arbitrary: the order of accesses can be anything, and the memory doesn't care.
Both kinds of semiconductor memory in this course are random-access:
The name "RAM" is historical: it was coined when the alternatives were tapes and drums, and it stuck as the name for read/write memory. A ROM is just as random-access as a RAM.
Random access is what the address decoder provides: it selects any word line directly, in one step.