In the original rating system from the 1670s, first-rates were ships of exactly 100 guns, but as time passed, ships were built with more guns, and they too were called first-rates.
Although nominally very powerful, first-rates tended to be slow and invariably expensive to operate. For stability, the lowest gundeck had to be very close to the water, and in anything but calm water the gunports had to be kept closed, rendering the entire deck useless. As a result, the few first-rates were typically reserved as commanding admirals' flagships.
These being the most powerful ships of the navy, it was common to compare them with the navies of other nations, and frequently one sees the largest ships of those navies being referred as first-rates, even though only the Royal Navy used the formal six-step rating system.
First-rate is also a common adjective used to mean something of the best or highest quality available.