Assuming the manufacturer has rated their equipment accurately and honestly, the wattage spec is useful in determining whether that particular piece of equipment is a good match for your speakers in terms of having sufficient power to drive it to SPL levels you find satisfactory in your listening room and also to decide whether your speakers and this amplifier are a proper match from a power output/power-handling perspective. Usually expressed in watts, this specification is probably the most often sought-out and compared number for amplifiers. Some specifications have a foot in each camp, so to speak, and serve both a practical and theoretical purpose.
Audio specifications fall into two broad categories: Those that are nice to know, from an enthusiast or intellectual standpoint and those that are genuinely helpful in assisting you to use, install or set up your equipment.