Etymology

Recorded since 1387 "to mark (a book) with chapter numbers or marginal references", from coter, from Medieval Latin quotare "to distinguish by numbers, number chapters", itself from quotus "which, what number (in sequence)," from quot "how many" (related to quis "who"). The sense developped via "to give as a reference, to cite as an authority" to "to copy out exact words" (since 1680); the business sense "to state the price of a commodity" (1866) revives the etymological meaning. The noun, in the sense of "quotation," is attested from 1885.

Verb

1. To refer to (part of) a statement that has been made by someone else.
2. To prepare a summary of work to be done and set a price.
3. To name the current price, notably of a financial security.
4. To indicate verbally or by equivalent signs that a quotation is starting

Noun

1. A quotation, statement attributed to someone else.
2. A quotation mark.
3. A summary of work to be done with a set price.

   After going over the hefty quotes, the board decided it was cheaper to have the project executed by its own staff

Usage notes

In a technical sense, "quote" is not a noun but a verb. "a Quote" has seen common use for well over a hundred years, however, so if you (mis)use it you are still likely to be understood and are unlikely to be corrected except in a highly formal or academic context.