The encrypted traffic inspection, or TLS interception, can occur because they present a certificate that is trusted by the client. This is usually because in a corporate environment, the network administrators have installed a root certificate into the list of authorities trusted by the client. The certificate presented to the end user is generated on the fly and the client essentially sets up a TLS connection to the middlebox. The middlebox then sets up a connection to the real server and proxies the data to the real server, inspecting it, and possibly modifying it.
With a modern version of TLS (1.2 or newer), it isn't possible to intercept data unless the TLS middlebox is trusted in this way; the protocol would be insecure if it allowed this otherwise.
A TLS middlebox in this approach can be a physical firewall device or a proxy, and additionally some antivirus and firewall programs, mostly on Windows, implement this functionality.
Note that cryptographic research has found that many TLS middleboxes contain security problems. For example, they may only support older, less secure algorithms or parameters; they may fail to validate certificates correctly or at all; they may not support the latest version of TLS; or they may fail to implement security-relevant extensions, like encrypted ClientHello. This is in addition to various cases where they are known not to implement HTTP properly and therefore break tools relying on it, like Git. Thus, unless you are sure your implementation doesn't suffer from any of these flaws, deploying such a middlebox is probably unwise.
It is possible to do some analysis on encrypted payloads. TLS supports padding, but it is less common with modern AEAD algorithms, so most connections leak some amount of information about the data being transferred. If the ClientHello is not encrypted, it's possible to receive the server name from the SNI extension, as well as information about the inner protocol via ALPN. These are used in some countries to implement censorship. Additionally, timing data is possible as well, but that is not always interesting. Provided you cannot decrypt the data, though, you cannot see what the actual content is.