Flutter allows developers to create visually appealing mobile applications for multiple platforms using a single codebase, and the integration of custom fonts can enhance the app's unique appearance and brand identity. The tutorial provides a step-by-step guide on how to add a custom font to a Flutter project, starting with downloading a font file, such as Montserrat, from Google Fonts, and then importing it into the project. It explains how to declare the font in the pubspec.yaml file, which registers the font for use throughout the app. To use the custom font, developers can apply it to the Text widget with the TextStyle property or set it as the default font in the MaterialApp's theme property, ensuring consistency across the app. The tutorial also notes the possibility of using the google_fonts package for runtime font fetching and caching, offering an alternative method for managing fonts in Flutter applications.