I've never heard that specific description/instruction related to breathing exercises. But I agree there is a feeling which I could describe as "compression" happening, so here are my thoughts on that. I'm Presuming you're doing "square" breathing (or similar), where you are breathing in for one "count" (however long that is), then pause with your airways open for one count, then out for one, then pause for one count.
In the second count, you are dynamically balancing the tension of your diaphragm muscle against your abdominal distension. During the inhalation you've progressively tightened your diaphragm muscles to pull air into your lungs. At the same time you're relaxing your abdominal muscles to let the surface of your abdomen move away from your spine -- making room for the abdominal contents being displaced by your diaphragm. When you stop the inhalation, there will be a sensation in your abdomen -- one could call it a sensation of compression.
Also, during the first count (inhalation), that sense of compression (again I don't like that description, but ...) would be increasing during the progress of the inhale as you progressively displace your abdominal contents through the movement of your diaphragm.
If you tense your stomach(abdominal) muscles, you'll constrict your inhale making the diaphragm work harder, and I think you'd be less likely to feel the compression we're talking about. My understanding is the abdominal/stomach muscles should be completely relaxed on the first(inhale) and second(pause) counts.