Definition
A proxy server is a middle computer that visits websites on behalf of your device. When you ask the proxy, it goes to the site, picks up the data, and hands it to you. So the site usually records the proxy's address instead of yours. Since it stands in the middle anyway, it can also filter connections and save data ahead of time.
I Asked a Friend to Run to the Convenience Store
Some days you want ice cream from the convenience store but don't feel like going out. So you hand some money to a friend who's heading out anyway and ask them to pick it up. The ice cream ends up in your hand, but the store clerk saw your friend's face.
You can make a similar request on the internet. Instead of your computer connecting straight to a site, you ask another computer in the middle to go for you. This errand-running computer is called a proxy server.
When you connect to the internet, the site on the other end sees a number tag from your device. This tag is called an IP address. Like a home address, it gives clues about what area the connection came from.
When you go through a proxy, the one that connected to the site directly is the errand runner's address, not yours. But some proxies pass along a note with the original requester's address, so it isn't always hidden. It's like the clerk remembering only your friend's face.
The Errand Runner Also Works as a Gatekeeper
Sending someone on an errand has one more perk. Right when the request comes in, they can filter it and say, "No, you can't buy that." That's why schools and companies set up proxies.
If all connections go through a single errand runner, you can stop people from heading to risky sites right there. A record of who went where also gathers in one place. That makes things much easier for whoever manages the network.
After many trips, the runner also picks up a trick. If several people ask for the same thing, the runner can buy it ahead of time and hand it straight to the next person. This copy saved in advance is called a cache.
Thanks to that, the wait gets shorter when many people view the same photo or file. The runner doesn't have to go all the way back to the store again.
A Little More Precisely
Handing off an errand is convenient, but your friend ends up knowing everything you bought. A proxy is the same. Which sites you visited stays right there on the errand runner's side.
That's why it's wise to be careful with a proxy when you don't know who runs it. If you trust the word "free" and connect to a stranger, you may end up handing the very information you wanted to hide to someone you don't know.
One more thing: a proxy usually handles only the errand you asked for. For example, you might give it just one browser window, while your other apps still go out directly as before. If you want to wrap up all the traffic your device sends and receives and carry it together, you need to pick a different method, such as a VPN. One errand runner can't solve everything.
Common misconceptions
If you go through a proxy, no one can see what you did on the internet.
Your address is often hidden from the site (though some proxies pass your address along), but whoever runs the proxy can see exactly where you went. The company that provides your internet line can also see the connection to the proxy itself.
A proxy server and a VPN are the same technology with different names.
A proxy usually handles only the traffic you point to it, like a browser window. A VPN differs in that it wraps all the traffic your device sends and receives and carries it together.
Where you meet it
When a certain site won't open on a school or work computer, a proxy in the middle is often what's filtering it out. Sometimes a firewall or domain blocking does it instead.
When many people download the same file, the copy the proxy saved ahead of time shortens the wait for everyone after the first person.
In one sentence
Because a proxy is a middle computer that visits sites for your device and hands you the data, it can hide your address, filter connections, and even help with speed.