Cryptocurrency exchanges are online marketplaces where you can buy & sell cryptocurrency.
Exchanges work similar to online brokerages, you deposit fiat currency (dollars, pounds, euros etc.) and use those funds to purchase your cryptocurrencies.
Binance is one of the largest online exchanges. It supports most commonly traded cryptocurrencies including ADA. https://www.binance.com/
Like most exchangtes Binance provides a crypto wallet for you to store your electronic funds. We suggest storing your ADA away from exchanges, read more in the linked article.
Kraken is LoftLad's choice. Not as HUGE as the others in terms of size and features, but it has a very intuative App and makes the whole process super simple. https://www.kraken.com/
Kraken also has a wealth of awesome information, check out this article for a starter https://www.kraken.com/en-gb/learn/what-is-cardano-ada/
"Coinbase is a well-known cryptocurrency exchange that makes it easy to buy, sell, and exchange cryptocurrency. Coinbase makes buying ADA as easy as buying a stock through an online brokerage, but look out for the fees and poor customer service" - Investopedia
Much like Kraken, Coinbase have an abundance of information and guides that are worth checking out https://www.coinbase.com/learn/tips-and-tutorials