How is it different :
My big son and My son is big?
My big son = ابني الكبير My son is big = ابني كبير
The first, the adjective is attributive (describing your son as "big") The second, the adjective is predicative (telling a fact about your son as being "big").
in Arabic, the (attributive) adjective follows the noun and mimics it in its conditions: gender, definition, and number. Since "my son" is (by nature) defined, even without adding "AL" (it is defined by the possessive article ي=my) then the attributive adjective (كبير) has to be definite -> الكبير (the big)