Watts is a measure of Power output. There are several Watts ratings including Watts RMS, Peak Watts, Total Watts, PMPO, and maybe others depending on what the Manufacturer uses to rate it's speakers. More watts usually means the Speakers will play louder although that is also a function of the Speakers sensitivity and that is tied into the Speakers efficiency which is based on speaker type, enclosure type, and internal volume.
as I understand it takes a doubling of power in watts to increase the sound level 3 db. A 3 db increase is about the amount needed for the avg. person to think there is a discernable difference in loudness. If you know your Speakers sensitivity at 1 watt. You can figure out it's loudness(Sound Pressure Level) given the power of your amplifier
as an example: a speaker with 88 db sensivity at 1 watt means the speaker will produce an 88 db signal(Sound Pressure Level) with one watt input usually measured on axis about 1 meter from the front of the speaker. To make the sound just discernably louder you need to double power to 2 watts for a 91 db level, 4 watts for 94 db, 8 watts for 97 db, 16 watts for 100 db, 32 watts for 103 db, 64 watts for 106 db, 128 watts for 109 db sound pressure levels and so on and on.
The Loudest Rock Concert ever recorded is Deep Purples "Made in Japan" album. supposedly SPL levels over 140 db were measured at the gig. assuming about a 90 db sensitivity for the guitar amps that would require about 262,000 watts of power. which they probably had if you've ever seen the pictures of the Marshall stacks on stage.
Hope this helps and I hope you enjoy your new speakers. It's how they sound that really matters. Watts be damned -lol-