A noun is the name of a thing. "A car." "A horse." "A man."
An adjective is a word that modifies a noun. It answers the question "What kind?" Examples: "A red car," "A fast car," "An old car." "Red," "Fast," "Old" are adjectives. What kind of car is it? A red car.
A verb is the name of an action. "To run" is a verb. (By convention in English we talk about verbs in the infinitive form, with the word "to.")
An adverb is a word that modifies a verb. It answers the question "how was the action done?" Many English adverbs end with the suffix "-ly."
"He runs quickly," "He runs well," "He runs gracefully." "Quickly," "Well," and "Gracefully" are adverbs. The answer the question "how did he run?"