'Compress' is Latin for 'press together' — the root 'premere' also gave us 'print' and 'espresso.'
To press or squeeze together, reducing the volume, size, or duration of something by applying force or pressure.
From Old French 'compresser,' from Late Latin 'compressare' (to press together), a frequentative of Latin 'comprimere,' composed of 'com-' (together) and 'premere' (to press). The Latin verb 'premere' and its past participle 'pressum' are the source of an enormous English word family including 'press,' 'pressure,' 'express,' 'impress,' 'depress,' 'oppress,' 'repress,' and 'suppress.' The PIE root is *per
The noun 'compress' (a pad pressed against a wound) and the verb 'compress' (to squeeze together) are the same word but entered English along slightly different timelines. The medical compress preserves the most literal sense of the Latin — physically pressing something against something else — while the verb drifted toward the abstract notion of making things smaller.