Have you ever thought about something you wanted or something happening to you so hard and so often that it happened? That's manifestation.
Manifestation is using thoughts, actions, energy, and words to create the world and environment you want around you. Manifestation is a conscious effort to trust that the universe, God, or any higher being you believe in will provide what you need and want.
Some people, at least in my experience, have an innate ability to manifest quickly and efficiently. Some people have a system for how they manifest even little things. For example, my own mother has a kind of ritual where she envisions herself giving a request to a being named Walter, and Walter will file that request to the universe. When the request is fulfilled, even if it's just finding a good parking spot in a busy parking lot, she always says out loud "Thank you Walter".
Manifestation is also about being grateful for both what you have, and what the universe has on the way for you. A bitter outlook will just bring bitter results.
But those are just my thoughts.