round

please refer to the definition of the word 'round' on the weblio dictionary.
you can find it at the definition of adverb 1-b.
b(a period of time) from beginning to end, all the way (cf. Preposition 7).
(all) (the) year round , all year round.

you can find similar phrase at the definition of the word 'around'
you can find it at the definition of adverb 4-b.
(all) the year around＝all year around