A general definition would be:
Compound words are formed by joining two or more free morphemes together.
Compound words consist of morphemes - to be more precise they consist of free morphemes. The only exception are the so-called cranberry words. They have a bound base like cran-. Many linguists do not put them under the categorie of compounds. Therefore we do not discuss these words.
We will deal with the 3 main groups of compounds: noun, verb and adjective compounds. Their constituents can be nouns, verbs, adjectives, adverbs and prepositions. Thus the compound itself and each constituent belong to an open class of words. An indefinite number of new words can be added to an open class of words and therefore compounds are not limited in number. Theoretically you can add as many free morphemes to another free morpheme as you like - compounding is recursive.
Compounds can also form other compounds, for example lakeside / Grammar School . Added together we get: Lakeside Grammar School.