The 4.5V to 18V supply range lets it operate from a 5V logic rail or a 12V industrial bus, though the low end of that range needs checking against the MOSFET's Vgs threshold.
The 1.5A source/sink rating determines how fast the driver can charge and discharge the MOSFET gate capacitance. A 1.5A peak into a 10 nC total gate charge (typical for a small TO-220 MOSFET) yields a transition time around 6–7 ns, well within the 25 ns typical rise/fall window. That keeps crossover conduction losses low in a half-bridge, but the designer still needs to budget dead time from the controller side — the driver itself has no built-in cross-conduction prevention. For larger dies (100 nC gate charge or more), the 1.5A peak will stretch the switching edge; consider a higher-current driver if the application runs above 200 kHz.
The 4.5V to 18V supply range covers the common 5V and 12V rails. The logic input thresholds are 0.8V (VIL) and 2.4V (VIH), so a 3.3V logic output will drive it cleanly as long as the high-level voltage exceeds 2.4V — most 3.3V CMOS outputs do, but check the actual VOH at the source current. At the low end of the supply range (4.5V), the gate drive voltage to the MOSFET is only about 4.5V, which may not fully enhance a standard-threshold MOSFET; logic-level or sub-logic-level MOSFETs are the right match here.