In more detail
TLS (Transport Layer Security) is the protocol that encrypts and authenticates connections between a client and a server. It is the "S" in HTTPS and also protects email, VPNs and many APIs. TLS is the successor to SSL, whose versions are all retired. A handshake agrees on keys and checks the server's Digital certificate, then the data is encrypted with a fast symmetric cipher. TLS 1.3 (2018) is the current version; TLS 1.0 and 1.1 are deprecated. See How HTTPS and TLS Work.
Why it matters
TLS gives three things at once: privacy (eavesdroppers see ciphertext), integrity (changes are detected) and authentication (you are talking to the real server, not an impostor). Problems show up as certificate warnings, handshake failures with old clients that only speak deprecated versions, or sites that quietly allow weak settings. An expired or mismatched certificate breaks trust even if the encryption itself is strong. The SSL certificate checker and the security headers analyzer look at a site's setup.
Example
Connecting openssl s_client to a local test server with a self-signed certificate reports:
Protocol: TLSv1.3
Cipher is TLS_AES_256_GCM_SHA384
Verification error: self-signed certificate
The connection is encrypted with TLS 1.3 using AES-256 in GCM mode, but the client does not trust the issuer, so verification fails. A public site would show a chain ending in a trusted authority. Related: HTTPS, Encryption.
Common confusion
"SSL certificate" is a leftover name; the certificates are used with TLS. HTTPS is HTTP carried inside TLS, so TLS is the lock and HTTPS is the web traffic inside it.