An instance is one of the sites on mastodon. Our instance is https://this.mouse.rocks. @Metaph@scalie.business is on https://scalie.business. Mastodon lets anyone run their own site and access the anyone else on any other Mastodon site.
If that is all sounding a bit too technical: Don't worry about it!
You only need to know your instance is this.mouse.rocks.
The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!