On the website:
The foods and recipes that you click the "I Like This" button on are added to a collection of Favorites for you. You can find these recipes and foods you've added to your Favorites Collection on the site by expanding the left sidebar (click the menu button at the top left) and clicking "Collections." Find the "Favorites" Collection in your Collections list and click on it to access these recipes and foods.
You can favorite("like") a food or recipe by clicking "I Like This" to add it to your Favorites Collection:

On the app:
The Favorites on the app are treated like a Collection. (The website will soon operate this way as well.) To add a food or recipe as a Favorite on the app, tap on the recipe/food to view its details page. Tap the star icon, then check off the box next to "Favorites" to add the food to your Favorites.
To view all of your Favorites, tap on "Preferences" at the bottom right of the screen, then scroll down and tap "Collections." From here, tap "My Collections" at the top, then tap "Favorites" to view all of the recipes and foods you've added to your Favorites list.