The new multiple link option is presently being tested with selected artists in the app, as seen in this example by hairdresser Sarah Page.
In the profile's link section, you can see that there is a 'and 2 others' sign to the right of the primary link, referring to the extra URLs listed. Tap on it, and you'll get a pop-up with numerous URLs, allowing you to send traffic to more sources directly from your IG presence.
This option has actually been under testing since October of last year, with versions of the format being evaluated in the app's back-end code.
It's unclear how many links users will be permitted to post officially, but the objective appears to be to diminish the utility of third-party programs like Linktree, which many IG users presently use to add more connections to their profile in the app.
Instagram has previously advocated Linktree, but it now appears that it is seeking to give more direct, native solutions to facilitate the same - which is likely bad news for Linktree.
There's also no official information on who presently has access, so you may be able to use this option right now, though it does feel a little incomplete, with the primary display of URLs likely slated to be updated more before a larger rollout.