From the Cloudflare Support website:
Q: Why do my server logs show Cloudflare’s IPs using Cloudflare?
A: When you sign on to Cloudflare the way your logs are displayed will change because Cloudflare
acts as a proxy. This means that your visitors are routed through the Cloudflare network. This
allows Cloudflare to stop attacks before they reach your network. It also allows Cloudflare to
speed up page load time by more efficiently routing packets and, more importantly, caching
static resources (images, javascript, css, etc.) on a very fast connection. However, as a
result, the connecting IP will always come from the Cloudflare network.
As a result, commenters’ IP will also be masked by Cloudflare. Luckily, Cloudflare sends the real
user’s IP in a separate header. This plugin saves it, as well as the user’s geo-location (also
provided by Cloudflare), and displays this information in the admin panel.
Note that when the blog is served directly to the internet (not through Cloudflare), anyone can
spoof any IP address and geo-location by specifying any value in the request headers.
Screenshots
The admin panel with the plugin activated