The Secure Sockets Layer does indeed refer to the operating system concept of sockets.
Sockets are a generalized form of inter-process communication. At the most basic level a socket allows you to read and write data to and from the socket just as though you are reading or writing a file, the difference is only that the source and destination of socket communications is another computer process rather than a file.
Sockets can be used to connect different processes on the same machine, or different processes on different machines. The interface is abstract by design so that the end programmer (you) don't need to worry about whether or not your messages are being passed through memory to another process over a local Unix-domain socket or whether they're going over an IP network or whether they're using UDP or TCP, etc.
However, the traditional sockets model doesn't let you know who is reading and writing the other end of the communications channel. Even within a single machine you can't be confident that there isn't some malware connected to the other end of your communications channel. This is much more true for internet-enabled sockets, which might read/write data from anyone in the world. Moreover, whenever your data travels over a physical medium, whether that's the RAM inside a machine or a copper wire, there's the chance that an adversary may be trying to intercept or modify your communications.
Thus, sockets provide the communication mechanism, but don't guarantee the authenticity of different parties to a communication, or the confidentiality of data passed through the sockets mechanism.
Transport Layer Security (TLS) and it's predecessor the Secure Sockets Layer (SSL) are solutions to the above problems. The TLS protocol can use public-key cryptographic solutions (e.g. signed certificates and trusted third parties) to guarantee that the process on the other end of a socket does indeed belong to the people who claim to own the socket, and it can use regular encryption to perform end-to-end encryption between the socket endpoints.
The difference between a regular socket and a secure socket in practice is that a regular socket is wrapped inside a secure interface, so the socket technology does not change but the wrapper guarantees that all communications sent over the regular socket are properly encrypted and decrypted.