The main purpose of piston rings is to provide a seal between the combustion chamber and the crankcase. If this sealing is not sufficient, the oil is no longer scraped off the cylinder wall down into the sump. Instead it accumulates until it enters the combustion chamber and is burned.
Damaged piston rings (due to dirt, lack of lubrication, heat, etc.) will provide insufficient sealing. Incorrectly installed piston rings after a recent overhaul will also result in insufficient sealing. This can be due to broken piston rings, jammed piston rings, incorrectly installed piston rings or overstretched piston rings (during installation).
Compression testing can be used to identify lack of compression (lack of sealing capability). If the compression is outside manufacturer’s specified range, and a wet test (compression testing with a small amount of oil added) increases the compression, then it can be indicator of damaged piston rings (but it also may be other components such as valves).