Floaters are Monster Cards that have replaced themselves in some way, allowing the player using them to generate card advantage. An example of a Floater is "Dekoichi the Battlechanted Locomotive." Because Dekoichi allows the player to draw a card, it has essentially replaced itself in the player's hand, losing the player no cards overall if it's destroyed or lost. Another example is "Gravekeeper's Spy." Spy replaces itself with a Monster on the field, as opposed to a card in hand, but the idea is the same; the player loses no overall card presence, even if the Floater is destroyed.
Currently, the most commonly used floater is "Reborn Tengu", a monster that Special Summons another copy of itself when it leaves the field while face-up (except if returned to the top of its owner's Deck or used as Xyz Material).