There are various resources needed for a computation, such as CPU, RAM, and maybe disk IO or network bandwidth. Typically for a given computation just one of these resources is a limiting factor, and the computation is said to be "bound" by that resource. For instance a CPU-bound task can be made faster by using a faster CPU, and an IO-bound task can be made faster using more/faster disks, but an IO-bound task will run at the same speed no matter how much faster you make the CPU. Here the author defines what they mean by "memory-bound" in the second sentence:
The more data that it can fit in the RAM, the faster the performance will be.
(I'm not saying that this statement is true, by the way, I'm just clarifying what it means)