Definiton
Operating systems have many consumers of memory: user allocations, file caches, network buffers, etc... Memory pressure happens when there is a shortage of memory. It represents the the work that Linux (or any other OS) does in order to manage and shuffle memory around to satisfy the system's many users.
Causes
Memory pressure is caused when someone needs memory. Usually, that memory is simply any free memory. At times, more specialized memory is needed and you can see pressure when there is lots of free memory of other kinds. A few examples of these special needs would be DMA-capable memory, physical contiguity for large pages, "low" memory, and memory on one NUMA node.
A common mistake is assuming that having any free memory means that there is no pressure.
FAQ
What happens because of memory pressure?
How do you tell you are under memory pressure?
How do I find the source of the memory pressure?