The term "floating" in electrical contexts means isolated, not connected. In the context of a power supply this may refer to a complete circuit not having any connection to some other potential, such as mains ground. Thus "floating" power supply outputs might be connected in series without causing a short-circuit, whereas this cannot be done if they are all grounded.
A floating logic input is simply open-circuit (not connected to a gate output, or anything else to define its level), although the common line feeding the gate may be grounded. The effect of leaving inputs open in this way depends on the technology used to make the gates: commonly this is an undesirable condition as the input level is not defined. This is particularly true for MOSFET inputs like CMOS, because they draw extremely low currents.
Sometimes a pull-up or pull-down resistor may be used to give a default condition to an input which is likely to be disconnected, to avoid the floating condition. Other technologies like TTL may have an inherent tendency to draw current input current in one direction, so that the input will more predictably take up one or other level.