Following the 802.11 Wi-Fi standard, you'll see a three- or four-digit number. This number indicates maximum link speed in Mbps. The higher the number, the faster the router.
In dual- or tri-band routers, this number is the combined speed (in Mbps) of all bands. For example, an AC1900 router class has a maximum of 600Mbps on the 2.4GHz band and 1300Mbps on the 5GHz band, adding up to a total of 1900Mbps.
Remember, in the real world, link speed is affected by a number of environment factors, such as walls, furniture, and appliances, so take manufacturer-reported speeds with a grain of salt. Also, like Wi-Fi standards, your router's speed is only as good as the speed provided by your ISP. If your internet speed is 150Mbps, that's the maximum speed you get regardless of the equipment you have. In that case, you probably don't need to waste your money on the fastest router on the market.
An exception to this would be for those who have fiber optic internet, which is becoming increasingly popular. Fiber optic networks have much faster speeds, can transmit across greater distances, and include a dedicated line for your residence, so you don't have to share with a cable provider. They also require investing in a router (and the right cables) that can handle this technology. In this case, it would be in your best interest to get a faster router.