Cloudflare is a content distribution network (CDN). I've worked for a few for a long time.
When you run a website, you're responsible for serving up web responses to every web request. Depending on the level of traffic that your website receives, that can involve paying for a lot of hardware infrastructure, plus a ton of money in hosting and transit costs.
So instead of buying a bunch of server hardware outright or paying long-term leases for cloud-based resources, you can use a CDN. CDNs have tons and tons of servers in data centers all over the world, all designed to hold onto a cached copy of your website data and serve it to customers. Because CDNs operate at a global scale, they get better deals on transit costs, plus traffic can be served from machines closer to where the end-user request is coming from so requests get fulfilled faster and with fewer errors.
There are a bunch of different CDNs out there: Cloudflare, Akamai, Amazon CloudFront, Fastly, plus plenty that specialize regionally (which can be important in network-constrained regions and restrictive countries).
Cloudflare tends to be a popular option due to speed, ease of integration and pricing.
The web acceleration component of the CDN business model isn't in a growth state right now. The web is entirely flooded with machine agents and bots generating traffic that website owners have to pay for, so there's big business in putting up roadblocks to prevent bot traffic (like Cloudflare's annoying 'are you a human?' checks).