There are already plenty of apps that let you play chess against an engine or online opponent on your smartphone. Analyzing your old games from time to time can help further improve your game. Analyze This Chess is a convenient app that brings Stockfish to your iPhone, allowing you to analyze and annotate your past games.
You can use this app to set up positions to see where you have made mistakes. You can paste any PGN or FEN via clipboard, add comments to your game, and share games via e-mail. The pro version allows playing against Stockfish. It also doesn’t have ads.
You can try this app for free but the pro version costs $2.99.