'pressed-in' ultimately derives from the verb 'press' (Modern English), via Middle English 'pressen' and Old French 'presser', which in turn comes from Latin 'pressare' (frequentative of 'premere'), where 'press-'/ 'prem-' meant 'to press or squeeze'.

'press' changed from Old French 'presser' into Middle English 'pressen' and later Modern English 'press'; the past participle formed as 'pressed' and combined with the particle 'in' produced the compound/adjectival form 'pressed-in'.

Initially it meant 'to push or squeeze' (physical pressure); over time compound uses like 'pressed-in' came to mean specifically 'made inward or sunken by pressure' or figuratively 'forced into a space or position'.