A proxy is a program people used to have on home and office firewalls that would cache requests from web browsers and similar software. The idea was to store objects from the world wide web in case they were needed at a later time. The advent of HTTPS just about everywhere has nullified the use-case for regular proxies.
Reverse proxies are proxies in the other end of a typical home users web connection. They sit between web servers and the customers accessing them forming a chain that looks like:
Many of the reverse proxies on the modern web are provided by large content delivery networks such as Cloudflare. Most modern web servers support being behind a reverse proxy. Most modern web servers can also be reverse proxies and some web software require a reverse proxy. As an example, the Searx search engine can't provide services to the web on it's own, it needs to be behind Apache or nginx or something else that handles the TCP connections going back and worth between Searx and the web browsers used to access it.