For an ISP the most important advantage of a proxy is probably the possibility of caching — if multiple users request the same static resources from popular sites, the proxy server can cache such resources and serve them to clients without contacting the original site every time, thus decreasing the external bandwidth usage for the ISP and page load times for users (if proxy servers are not overloaded to the point that they are slower than origin servers).
Some ISPs go even further — they intercept all outgoing connections to the TCP port 80 (standard port used by HTTP) and redirect them to their transparent proxies; in this case clients do not need to configure anything in order to use the ISP-provided proxy. However, such behavior can introduce problems (e.g., it is likely that the site will see the IP address of the proxy server as the source of requests instead of the real client IP, and if one misbehaving user annoys site admins to the point of getting an IP ban, this ban will affect lots of other users of the same proxy server).
There is also a possibility to perform access control (or Internet censorship, as you may call it in case of an ISP performing it) using proxy servers; this could provide more fine-grained control than IP-based filtering for unencrypted HTTP requests. However, in this case using the proxy needs to be mandatory (in the ISP case a transparent proxy intercepting all unencrypted HTTP requests will probably be used).