Sometimes, a creator wants to make an important object more noticable and important looking. Along with having it glow or spin, one of the most effective ways is having the object levitate.
This object is usually a MacGuffin
or other plot device, but may be a more mundane item or powerup if the trope is invoked in a videogame. The degree of floatiness varies, from being affected by gravity but recoiling from touching anything else (the ground, a protagonist's hands etc) to being completely unaffected by gravity.
Often goes hand in hand with Power Glows and Everything's Better With Spinning.
Note: more examples needed, this is just the start of the page.
Anime and Manga:
The titular Laputa from Laputa: Castle in the Sky is...Well...A floating castle. It's also pretty vital to the plot, surprise surprise.
The cards from Cardcaptor Sakura often float. There is also a card that makes other things float, called (you guessed it) the Float Card.
The Matrix of Leadership and the Space Bridge control pillars from the Transformers films were capable of hovering. Indeed, the Space Bridge pillars actually enter orbit.
Most games featuring powerups probably have a few of them floating.
The rings from the Sonic series float and spin just above the ground. In some games there are also powerup boxes or balloons in midair.
In Final Fantasy XIII and XIII-2, the treasure spheres float and spin, coming to rest once opened. In XIII-2, some of the artefacts float gently above the ground or holder's hands.