Server side request forgery is a vulnerability where a server connects to an arbitrary host supplied by the attacker.
When testing it is useful to have a host available on the internet where the server can connect to. This will typically not work with your home or work PC, because it is behind a firewall or behind NAT. If the server connects to your IP address, your router will block the connection. Ideally you would have a server with a public IP address, such as a VPS with a hosting provider. Alternatively, you could configure port forwarding in your router.
An alternative is to use a third party service. For example, the Burp Collaborator is a server that will notify you of any interactions with it.
Note that it is not necessarily a vulnerability if a remote server connects to your server. The vulnerability comes if the server exposes information from the local network it is in. Then you can exploit the "server side" of SSRF to navigate the network that you can't normally reach.