There have been plenty of apps for iPhone and iPad that allow you to connect to a remote server, via ssh for example. I use a mix of Termius and Prompt for these. But now there’s a new, if simple, app in town that gives you a local shell on your iOS device.
The simple yet properly named app called Terminal by Louis D’hauwe currently only includes some basic commands, so you won’t (yet?) find your whole collection of tools. In it’s current status it feels like a great start with hopefully many more features to come in future updates, mostly the mentioned toolbox you can find on most Linux/Unix machines.
Terminal is a free download on the App Store. You can also find the source on GitHub which gives me even more hope that new features will be added quickly.
Update, March 4th, 2019: Since I see quite a few people coming this way, iSH is another app you should check out. They also have open TestFlight invitations right now, so you can try out the newest features before they become available in the final version on the App Store. OpenTerm by Louis isn’t available anymore since he joined Apple.