Compression in computer terms is a process of re-encoding binary data into a form that uses lesser bits than the original data. It helps save storage capacity, decrease cost for network and hardware bandwidth and speeds up file transfer.
Since it involves replacing symbols for larger patterns of data, it can be a “hard problem” for computers because it becomes hard to find out whether or not the compression found is optimal. By optimal, I mean, if you kept on trying, would it get better?
I once had an experience compressing an assigned poem that was given as a class assignment. I realized how progressively easy it was compressing, but at a certain point, the dictionary and the scale tips started to get so big that I lost the benefit of having it.
It is difficult to know when to stop and difficult as well to verify when you have compressed it the most because it would take an unreasonable amount of time. However, you can use “heuristic” to identify some rules when the solution becomes good enough.