A floater is a Monster Card which has replaced itself in some way, allowing the player using it 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.
Many modern monsters, especially Extra Deck boss monsters, float to provide an easy way to recover from removal effects. Such monsters are powerful due to the fact that merely by being Summoned, they have fulfilled their duty and the player will not lose advantage from their loss, allowing them to be used aggressively with less risk. The "Duelist Alliance Format" was particularly famous for the amount of floating effects in the metagame, with many Duels becoming highly technical grinds as each player sought a way to break through their opponent's replenishing defences.