Historically, proxies were used as ways to bypass things like location-based content restrictions and to anonymise your web browsing. More recently though, every service offering those functions has called itself a VPN or Virtual Private Network. Proxies and VPNs are similar in concept but have fundamental differences.
Proxies are used to relay traffic through a specific “proxy” server. This proxy server acts as a go-between middleman, it replaces your IP address with its own and then forwards the traffic on. This means any traffic you send appears to come from it. It’s effective at bypassing location filters. VPN’s do exactly the same thing, you relay your traffic through them, so it appears as if your traffic is coming from them.
The way you connect to a proxy, however, is very different to your connection to a VPN. A connection to a proxy is very lightweight, no extra data needs to be added (although some offer authentication), all the proxy does is change the source IP address information and forward the traffic on to the destination and returns the response in the same manner.
A VPN connection is encrypted, meaning that all data transferred between you and the VPN server is securely encrypted and can’t be read or modified by your ISP or anyone else. This adds a little extra overhead in terms of processing power, although on modern computers you shouldn’t be able to notice much of a difference unless you’re connecting to a server most of the way around the world.
When it comes down to it, a VPN can almost always replace a proxy. However, a proxy can’t provide the same privacy protections and security features that a VPN can. The VPN has realistically replaced the proxy.