HTTP Proxies are built on top of HTTP (the Hypertext Transfer Protocol) and can be pictured as a server that sits between you and the destination. In other words, compared to a reverse proxy, HTTP proxies take a request, forwards it to a server and proxies the reply back to you.
In the diagram below, you can see an example request:
HTTP proxy, by nature, can read request information and data that is sent back. As such, various actions can be performed: content-blocking and compression. Compression can help accelerate requests from a destination by further compressing information, while content-blocking can remove advertisements, or act as a filter for a child's Internet access.
Unfortunately, HTTP proxies are not designed to forward HTTPS -- or secure -- data. Such requests break the "trust chain" between a client and a server; in other words, data is NOT secure when going through an HTTP proxy. The data is decrypted on the proxy, and is re-encrypted, albeit using a local/self-signed certificate.
(This also means that HTTP proxies, by nature, are transmitting data in plain text. )
HTTP proxies offer negligible performance benefits and are (essentially) a middleman for data. They should not be used for secure data, as the vast majority of public HTTP proxies don't support HTTPS traffic.
HTTP is a protocol used to connect to web servers by web browsers to request content to view. This is also used to transfer larger files, and is often used for software updates.
A proxy is a medium (server) that forwards traffic to a requested destination and vice-versa.