There are a couple ways. The method most musicians have used since the mid-90s is phase cancellation, where you take an instrumental and use it to cancel out any sound that isn't instrumental (a-la noise-cancelling). In more dire scenarios, people would split the stereo tracks and cancel them against one another, which actually worked fairly well if you had a DAW precise enough to pull it off.

Then in the mid-2000s there were a few attempts to use algorithms for this (that mostly failed) and circa-2015 we started to see machine-learning based options like Spleeter and Demucs. This is what Apple is implementing here, and it's been freely available for years. It's not really novel for anyone who isn't writing their music on an iPhone.

I mostly ask because I've spent the past 2 or 3 weeks working on a remix album, and haven't really had trouble finding stem separation tools that work well.