This question could be an entire book, and there are several good books on the topic. I'll provide a pretty brief overview and then if you have follow-up questions, let me know. (My user profile has some previously answered threads and book suggestions.)

• Administration: Over the course of the 16th through 19th centuries, England/Britain built up a fairly robust naval administration consisting of standing offices that dealt with many of the common issues related to providing for a navy (victualing, ordnance, construction, dockyards, ropeyards, pursery, etc.). The Admiralty and associated boards were never perfect, but they created a climate in which it was possible to keep standing fleets at sea starting in the latter part of the 1600s.
• Technology: There was a strong tradition of innovation in British shipbuilding (to contrast with the French, for example, who had academic studies ahead of the British but were slow to adopt technological improvements like coppering ships and using wheels for steering). In addition, the English/British dockyards were the first to have a robust infrastructure of wet and dry docks, pools to keep ships in over the winter, and storage for construction materials.
• National commitment: The connection between piracy, naval daring and Protestantism that was forged in Queen Elizabeth's time became a strong part of English and later British national identity, and made the Navy the senior service in the English/British military.
• Unification: Britain was never free of the worry of rebellion or invasion, but unification with Scotland and the lack of any coherent Irish naval presence allowed the British to focus its attention on the navy, and not have to worry about a large standing army in the same way continental powers had to.
• Wealth from trade: There was a virtuous feedback loop where navies supported merchant fleets, which brought trade income to Britain, which allowed it to support a navy. A navy is the most expensive of the military services to maintain, and Britain's ascendance allowed it to expand its navy, which opened up more trade.
• Experience at sea: The English/British tradition (after the late 1600s, in any case) led it to promote officers only after they'd had significant experience at sea, which meant that its commanders were generally more experienced than those in contemporary, enemy navies. The old tradition of sailors sailing and soldiers commanding ships started to change in the era of Drake and Raleigh, and was thoroughly extinguished fairly early in the 1700s.