Take a look at the substantial but easy to understand presentation of Monero, that has been given recently by the xmr.to team at Bitcoin Meetup Switzerland.
To remind of, xmr.to is a specific exchange that allows users to make Bitcoin payments with the strong anonymity provided by Monero. This means that using Monero together with xmr.to, you can pay any Bitcoin address anonymously. You may find more onĀ https://xmr.to/