Top dressing is feeding the plants from the top - sort of. Think about it like this - if you are using liquid ferts they run into the soil with the water they're mixed with. When you top dress, you put nutrient dense material on top of the soil. When you water, the water washes some of the good stuff in. I did a little top-dressing this week with some worm castings, a little high phosphorous Indonesian guano, and some yum-yum mix. I just scratched it into the top inch or so of soil with a seldom used carving fork.
Many of the things folks use to make teas can also be used to top dress: compost, rock dusts, guano, castings. etc. The idea is that when you water, you gradually wash snacks deep down into the soil to feed the plants. There is some logic to top dressing. If a bird takes a dump it falls from the sky. It lands on the soil and gets washed in by rain. In the forest, leaves and stuff that compost land on top of the soil. As it rains it washes the nutrients deeper and deeper into the soil.
In an outdoor garden, top dressing often serves two purposes - it feeds the plant from above and can also help hold in moisture. A layer of composted mulch around the top of the plant feeds it continuously, and prevents evaporation from the soil.
I would say the down-side to top dressing is it makes it difficult to know exactly how much of what you're feeding the plants and their microbial sisterhood. But, when you look out past the property line and see all the stuff growing there, it is all fed by top dressing, and not by chelated liquid fertilizers.
