How does a GSM network connect to the outside world (PSTN, data networks)?

The MSC is the gateway to the outside: it links to the PSTN (traditional phone network), data networks, and signaling systems. For incoming calls a special role called the GMSC (Gateway MSC) is used.

The GSM architecture, top to bottom:

PSTN/ISDN   Data networks   Signaling systems
        \\        |          /
              MSC  (+ HLR / VLR / AUC alongside)
               |
              BSC
            /  |  \\
         BTS  BTS  BTS
               |
              MS

In the basic architecture the MSC itself connects directly to the external networks. The GMSC is not a separate box for every connection — it is the role an MSC plays when it acts as the entry gateway for traffic arriving from outside the operator's network.

External connections of the MSC:

• PSTN/ISDN — for calls to/from landline phones
• Data networks — for data services
• Signaling systems — SS7 signaling for inter-operator communication (roaming, call routing between networks)
• Other MSCs — for calls between subscribers in different areas

The GMSC (Gateway MSC) role: When someone calls a mobile number from a landline, the call first reaches the GMSC, which queries the HLR to find out where the subscriber is, then routes the call to the correct serving MSC. So the GMSC is the "front door" for incoming calls — the point where an outside call enters the mobile network and gets pointed at the right MSC.

Go deeper:

• Network switching subsystem (Wikipedia) — the MSC/GMSC core: how the gateway MSC interfaces the PSTN and queries the HLR to locate the called subscriber.