'appealability' is formed in Modern English from the verb 'appeal' + the nominalizing suffix '-ability' (from Latin via Old French); 'appeal' itself comes via Old French and Latin.

'appeal' derives from Old French apeler (Middle English appelen/appeelen), ultimately from Latin 'appellare' meaning 'to call upon, address'; the productive suffix '-ability' comes from Old French '-abilite' and Latin '-abilitas', and together they produced the Modern English formation 'appealability'.

Initially Latin 'appellare' meant 'to call upon or name'; over time 'appeal' developed the specialized sense of 'apply to a higher authority for review', and the derived noun 'appealability' now means 'the capacity to be appealed'.