The same term is used in two unrelated senses, and search results mix them freely.
Meaning one: an intercepting proxy
In networking, a transparent proxy sits on the path and catches traffic without the client being configured to use it. Company networks, schools, hotels and some ISPs use them to filter or cache web traffic. You did not set a proxy, but your requests pass through one anyway. For HTTPS they can see hostnames but not content, unless the device was set up to trust the network's certificate.
Meaning two: a proxy that reveals you
On proxy lists, "transparent" is the lowest anonymity level. The proxy forwards your requests but adds your real address in a header such as X-Forwarded-For, and usually announces itself with a Via header. The site sees the proxy's IP and yours. Above it sit anonymous and elite proxies.
How to check the second kind
Send a plain HTTP request through the proxy to a header echo:
curl -s -x http://USERNAME:PASSWORD@HOST:PORT http://httpbin.org/headers
If your own public IP appears anywhere in the returned headers, the proxy is transparent in this sense. Use an http:// target: over HTTPS the proxy cannot add headers, so the test tells you nothing.
Common confusion
The two meanings share only the idea that something is "transparent" to someone: to the client in the first case, to the website in the second. For a proxy buyer, the second is the one that matters, and no commercial proxy should behave that way. It is common on free proxy lists, which is one more reason to test before you trust one.