The second declension is a category of nouns in Latin and Greek with similar case formation. In particular, these nouns are thematic, with an original o in most of their forms. In Classical Latin, the short o of the nominative and accusative singular became u.
Both Latin and Greek have two basic classes of second-declension nouns: masculine or feminine in one class, neuter in another. Most words of the former class have -us (Latin) or -ος -os (Greek) in the nominative singular, except for the r-stem nouns in Latin, and the "Attic" declension and contracted declension in Attic Greek (when these groups are considered part of this declension). The latter class, i.e. the neuter nominative/accusative singular, usually ends with -um (Latin) or -ον -on (Greek), matching the accusative of the former.
The Wiktionary appendix Second declension contains more detailed information and full paradigm tables for the Latin second declension.