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The inrush current limiting function controls the slew rate to reduce inrush current.
Once a load switch IC turns on, its output voltage increases instantaneously, causing overshoot that might exceed the rated voltage of the load IC or circuit.
In addition, a large inrush current flows into the load switch IC to charge the output smoothing capacitor connected to the VOUT pin. Inrush current occurs during the period from the time when the load switch IC turns on to the time when the output voltage stabilizes. If the VIN pin is connected with a board trace with large impedance, the input voltage might sag because of a voltage drop that occurs across the trace impedance due to inrush current. This makes the load switch IC unable to provide a normal output voltage level.
After the load switch IC turns on, the inrush current limiting function raises the output current slowly to limit the inrush current, thereby suppressing the output voltage overshoot and the input voltage drop. Therefore, inrush current limiting helps improve system stability.
Inrush current limiting is also called slew rate control or soft start.

Load switch IC without an inrush current limiting function
Load switch IC without an inrush current limiting function
Load switch IC with an inrush current limiting function
Load switch IC with an inrush current limiting function

The following links also provide descriptions of inrush current limiting:

Application note: Basics of Load Switch ICs

FAQ: How can I suppress inrush current with a load switch IC?

Chapter2 Convenient functions load switch ICs

2-1. Useful functions available with load switch ICs
2-2. Operation of overcurrent protection
2-3. Operation of thermal shutdown
2-5. Auto discharge
2-6. Undervoltage lockout (UVLO)
2-7. Reverse-current protection

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