These "floaters" are actually tiny bits of blood vessels left over from when you were a fetus! As your eyes developed in the womb, blood vessels had to get to the cornea and lens so that they could grow properly. Once they eyes were fully developed, the blood vessels died and fell apart. However, your eye is a closed sphere, and the blood vessel pieces could not get out of the eye or be broken down by the immune system. As a result, the pieces usually sit on the bottom of the eye, not interfering with your vision. If you shake your head, though, they will float around like the snow in a snow globe and pass through your field of vision, creating the unusual objects you see.
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Those are usually called floaters. They're bits and bobs floating around in your eye fluid, and that's nothing unusual.