All Romance languages descend from a Latin parent, and many words based on Latin are found in other modern languages such as English. Moreover, Latin was a lingua franca, the learned language for scientific and political affairs, for more than a thousand years, being eventually replaced by French in the 18th century and English in the late 19th. It remains the formal language of the Roman Catholic Church to this day, which includes being the official national language of the Vatican.
Latin has an extensive flectional system, which mainly operates by appending endings to a fixed stem. Inflection of nouns and adjectives is termed "declension", that of verbs, "conjugation". There are five declensions of nouns, and four conjugations for verbs. The six noun forms (or "cases") are nominative (used for subjects), genitive (show possession), dative (indirect objects), accusative (direct objects), ablative (used with some prepositions), and vocative (used to address someone).
Romance languages are not derived from Classical Latin but rather from Vulgar Latin. Latin and Romance differ (for example) in that Romance had distinctive stress whereas Latin had distinctive length of vowels. In Italian and Sardo logudorese, there is distinctive length of consonants and stress, in Spanish only distinctive stress, and in French even stress is no longer distinctive.
Another major distinction between Romance and Latin is that Romance languages, excluding Romanian, have lost their case endings in most words (some pronouns being exceptions). Romanian is still equipped with several cases (though some, notably the ablative, are no longer represented).
English grammar is not a direct derivative of Latin grammar. Attempts to make English grammar fit Latin rules -- such as the contrived prohibition against the split infinitive -- have not worked successfully in regular usage. However, as many as half the words in English come to us through Latin, including many words of Greek origin, not to mention the thousands of French, Spanish, and Italian words of Latin origin that have also enriched English.