Fun with Chess is an iOS app that is a nice match for kids wanting to learn how to play one of the world's greatest games. It is not a typical chess experience, because it adds in factors of luck which limits your piece's moves with a roll of the dice.
The game keeps score, so you can play another person and decide a winner at any time. You can play the computer, another person face-to-face or remotely. There is a built-in chess tutorial, and a linked video with more information.
To make Fun with Chess more appealing to beginners, games are limited to six pieces and six applicable rules. I suppose one could complain that this is a chess variant, rather than a standard game, but I think it is less intimidating to someone just starting out, and a good way to learn the rules.
I played the game against the computer a few times, and while it is not playing at grand master level, it gave me a pretty good run. I did not try remote play.
Another option for beginning chess players is Chess Prime HD which is also free. It shows legal moves and has other support for novices. It is a more traditional chess game, and allows play against the computer and a human opponent.