I am writing about individual parts of the crypto world as if they are discrete. They are not discrete but I like to see the function of each part as separate, it helps me to see clearly.
Holding crypto is a matter of having the right series of numbers, something that is simplified through software in wallets. Trading crypto is the ability to buy crypto with fiat currency ($, €, etc), exchange one crypto currency for another or buy fiat with crypto.
Buying crypto with fiat or selling it back relies on using banks, and so is subject to bank charges, regulations and delays that can be imposed at any time.
An exchange is one way to trade one crypto for another. The user creates a trading account on the exchange and then can transfer crypto from a wallet for trading. The exchange does not normally buy and sell the crypto directly, it is a market place where traders put in buy or sell requests. So when you want to exchange crypto (e.g. exchange bitcoin for etherium), you are relying on another trader who wants to make the same trade reversed. The exchange simply facilitates it by hosting the traders’ accounts and charging for the service.
Once you start trading in crypto you see the benefits of a market that is open 24/7, has fast trades and low costs. It doesn’t help you choose your strategy, though, as it’s easy enough for the crypto that you are hodling to drop hugely in value in a matter of minutes.
Using an exchange can be very exciting, though, especially if you can learn to control your emotions and follow a trading strategy.
This is a very simplistic view of exchanges, it is supposed to help by giving an overview of its place in the crytpo world