5.5 mOhm Rds(on) — the conduction loss number that matters
That is the condition you design your thermal budget around. At 60 A full load, expect the dissipation to climb — the 110 W maximum power dissipation rating at the case tells you this part needs a good heatsink or forced air to stay within the 175°C junction temperature limit. The gate threshold voltage maxes out at 3 V at 250 µA, so a 5 V logic-level drive will turn it on, but the Rds(on) will be higher than the 10 V figure — the drive voltage range is listed as 5 V to 10 V.
This makes the STP120NH03L suitable for environments with extreme thermal cycling, such as under-hood automotive, industrial motor drives in hot enclosures, or power supplies in outdoor telecom cabinets. The 175°C ceiling gives extra headroom for derating when the case runs hot.
Gate charge and input capacitance — what drives the switching speed
These numbers tell you the gate driver needs to source and sink enough current to switch the MOSFET quickly. A 77 nC gate charge at a few hundred kHz is manageable with a standard gate driver IC, but at higher frequencies the switching losses will dominate. The ±20 V maximum gate-to-source voltage gives you room to drive it hard without worrying about oxide breakdown.