The idea is to add a little creaminess, a little luxuriance, to your dish, but without rendering it heavy. This can bring a simple pasta with, say, olive oil, garlic, herbs, and cherry tomatoes to the next level.
Here's how you do it: when your pasta is ready, strain it and quickly return it to the pot (or to a separate bowl). Crack an egg over the pasta, and mix it in vigorously. The result should be a kind of airy creamy sauce (it should not be little bits of scrambled eggs). This essentially is the technique you use to make carbonara: add a bunch of cheese and bacon and you've got that dish. But add instead some veggies sauteed in olive oil, and finish with just a touch of parmesan, and you've got a brilliant summer dish: light and delicious, with just the slightest hint of decadence. Try it with ripe bell peppers, or with shredded zucchini brightened with lemon.
One more advantage of this technique: it does great things to whole wheat pasta, which I don't normally love.
Here's my current favorite way of using this idea. It hardly seems like it necessitates a recipe, but here it is. Use about 1 egg for every 1/2 pound of pasta.
Heat water for pasta. Add pasta when water is boiling.
Meanwhile, heat olive oil in a skillet and chop a bunch of garlic. Cook (along with some dried hot pepper, if desired) until garlic just turns golden.
Add in a splash of white wine, a couple tablespoons of the pasta water, some salt, and let cook for a few minutes. Add fresh herbs just a couple minutes before the pasta is done.
When pasta is ready, quickly drain, return to pot, crack an egg over the pasta, and mix vigorously for about 30 seconds. You should have a light, airy creamy sauce.
Add some halved cherry tomatoes and the garlic/oil/herb mix and toss all together.
Finish with a little parmesan and some fresh ground pepper, and serve immediately.