In Latin nouns and pronouns are marked not only for case but also for number (Numerus). The number marking in principle corresponds to the number of entities referred to (e.g. unus filius/duo filii); exceptions are, for
instance: `pluralia tantum': e.g. tenebrae `darkness', and `singularia tantum': e.g. lac `milk'.  Number is, therefore, a semantic category.
Generally, nouns are not marked for the category of (grammatical) gender (Genus). Exceptions are certain nouns which indicate animate beings, such as filius/filia; productive suffixes are e.g.-tor/-trix. There is extensive literature on the nature and origin of the grammatical gender of nouns. Most linguists agree that, in spite of the existence of cases like -tor/-trix and many rules in Latin of the type `names of trees are feminine', there is no relation between natural gender (sex) and grammatical gender,  and, more generally, that there is no semantic basis for the gender of nouns.  Much more remarkable is, for instance, the relation between declension type and gender (e.g. `3rd-declension words ending in -s are generally feminine').
Agreement of adjectives, pronouns, etc. consists in the visibility of explicit (case, number) and implicit characteristics of the Head nouns in the form of these adjectives, pronouns, etc. Agreement of adjectives is a grammatical phenomenon which serves to show the coherence within noun phrases, even if such noun phrases are discontinuous.
Pinkster, Harm (1942-) , Latin Syntax and Semantics [info], xii, 320 p.: ill.; 24 cm. [word count] [Pinkster].