Why do companies use a web proxy, and what does it make possible because it terminates connections?

Question

Accepted Answer

So that not every workstation needs a public IP address: many clients with private addresses reach the internet through one access point. Because the proxy terminates the connections, it can also break up TLS/SSL encryption and see the content of the connection.

* Two connections instead of one: between them, the proxy sees the content in clear text. *
Practically every workplace has a browser with internet access. With a proxy, the browser does not connect to the web server itself; it asks the proxy, which opens its own connection and passes the result back. Two connections instead of one is the key: the proxy sees the request and the response in clear text (after decrypting, for HTTPS), so it can inspect them.
Breaking TLS has a cost: the proxy must present its own certificate to the browser, so the company's clients must trust the proxy's certificate authority, and the proxy must validate the real server's certificate properly, or it weakens the very security it intercepts.
Go deeper:

Proxy server — Wikipedia — forward and reverse proxies, the gateways that inspect what crosses.
 CISA — HTTPS Interception Weakens TLS Security — what goes wrong when an intercepting proxy validates certificates badly.