The quality or state of being compressible; the degree to which something can be compressed.
From 'compressible' plus '-ness' (state or quality). It's a straightforward formation describing the property of being squeezable.
This word rarely appears in modern English because scientists prefer the shorter 'compressibility'—but medieval writers loved stacking '-ness' suffixes to emphasize qualities.
Complete word intelligence in one call. Free tier — 50 lookups/day.