Meaning of “inch” - Learner’s Dictionary

inch

noun [ C ] uk us /ɪntʃ/

B1 (written abbreviation in.) a unit for measuring length, equal to 2.54 centimetres

not budge/give an inch informal
to be every inch sth

to be a particular kind of person in every way:

He is every inch a gentleman.

(Definition of “inch noun” from the Cambridge Learner’s Dictionary © Cambridge University Press)