It refers to the style in which someone walks. If you are tired, or depressed, you tend to walk 'flat-footed', or shuffle. If you are more energised, or excited, you tend to walk more 'bouncily' - your body moves up and down more as you walk. That bouncing, or springing is what those expressions are referring to.

You're on top of the world, you're bright eyed and bushy tailed. Jaja, acabo de explicarte una expresión inglesa utilizando dos más. En español significa caminar con brío según el diccionario. Espero que te haya ayudado.

Imagine you have springs in your legs, especially in your ankles, then walk. If you are in a good mood, you'll glide quickly, up and down. Usually people smile when walking like this :)