There were a few factors before the war and during the war that led to the dominance of the US Navy.
After World War I, the Washington Naval Conference of 1921-1922 led to the Washington Naval Treaty. The conference was intended to stop the naval arms race that had been going on between the victors of WWI - it limited the construction of battleships, battlecruisers, and aircraft carriers.
Both the British and Americans were limited to 525,000 tons of capital ships and 135,000 tons of aircraft carriers. Japan was limited to 315,000 tons of capital ships and 81,000 tons of aircraft carriers. In addition, there were limitations to the size of guns (16 inches max) and tonnage of battleships (35,000 tons).
This led to a lot of things - the Royal Navy once had a much more powerful navy than the US and now they were on equal footing. Furthermore, countries got clever to get around these restrictions - many capital ship hulls were converted to other uses (e.g. the aircraft carriers USS Lexington and Saratoga started off as battlecruisers) and in some cases, like the Japanese Yamato and Musashi, the treaty was outright discarded after a few years as the WW2 seemed likely.
In addition, during WW2, the overwhelming industrial and geographical advantage of the US helped the US Navy eclipse the Royal Navy.
For one, British ports were in range of German air attacks and the British Navy was spread out across the world defending its colonies. A lot of British ships were lost as they were scattered without sufficient air cover. Famously, the HMS Prince of Wales and HMS Repulse were sunk by Japanese aircraft in the South China Sea a few days after Pearl Harbor.
Also, the British were focused heavily on combating the U-Boat threat in the Atlantic so their focus shifted to smaller ships like destroyers.
The US didn't have to worry about those things - it had two giant coastlines far from any threat where they could build ships of all sort. The US also had a continent's worth of resources at its disposal - the steel industry was supreme in the US. Ships were produced at ridiculous rates - most famously, the Liberty Ships were built at an average rate of 42 days with a total of 2,710 of them built.
By the end of the war in 1945, the US Navy consisted of over 70% of the world's total numbers AND tonnage of naval vessels > 1,000 tons. They Navy was larger than the rest of the entire world's navies combined. Simply put, the numbers are staggering in every way imaginable:
A lot of it had to do with World War 2 and you could even argue as far back as World War 1. It would come down largely to a couple of factors.
First, the drain on the Brit's during both wars would take its toll on aspects, including their naval power. The United States, not being directly in the warzone would not suffer the same destructive effects.
Secondly, the industry. America's industry kicked into high gear with the government taking over control of these processes. 'Total War' was a term used to describe this. Everything was devoted to the war effort and run at a pace which allowed the Americans to literally pump out machines of war, such as powerful naval vessels. Fighting their way across the Pacific only helped them see the need for a more powerful navy.
As a result when the war came to a close, the US Navy would emerge on much better footing than that of the British. The Brits could simply not keep up with the machine of the US.