Inrush current typically refers to the transient current "inrush" as a result of a piece of equipment's capacitor bank on the power input. At initial power up of a device, its capacitors will have zero voltage across them (Assuming it has had enough time to bleed through parasitic or purposeful resistance to ground...) As a result of the caps being at 0V, they will act like a short circuit to the input power for a short time. There are many inrush limiting products, many of which need to be switched out of the circuit once the power inrush is over, such as thermistors and resistors.
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