To understand why Dreadnought was so revolutionary, you need to know how battleships that pre-dated her worked. Such ships, termed pre-dreadnoughts, would generally mount four large bore guns (11-12 inch) in two separate turrets, one forward and one aft. These would be supplemented by smaller guns, in the 7.2 - 9.2 inch range, mounted in four to six twin turrets. They would then have a secondary battery of guns for anti-torpedo boat use, usually 4-6 inch. This system had many flaws. The mixed calibre main battery confused fire control - there weren't enough large-calibre guns for proper salvo firing, the smaller guns couldn't be used for effective spotting due to the difference in calibres, and if all guns were firing at once, it could be difficult to determine which set of guns had caused which set of shell splashes. An RN observer aboard Togo's flagship at Tsushima stated that "when 12 inch guns are fired, shots from 10 inch guns pass unnoticed, while, for all the respect they instill, 8 inch or 6 inch might just as well be peashooters". The variety of calibres meant a higher share of displacement had to be devoted to the guns, reducing armour protection and speed. In addition, the increased magazine space required posed a major fire risk. They also had issues with their engines. They used reciprocating steam engines, which were unreliable, and could not sustain high speed - British squadrons steaming at 14 knots could expect breakdowns after just eight hours. Their maximum speed was 18-19 knots, but if they spent four hours at this speed, they could expect to spend up to ten days repairing and adjusting bearings. Pre-dreadnoughts were expected to fight at close range (British ones were even fitted with a ram bow) and their armour scheme matched this expectation.

Dreadnought solved all these problems and more. She was fitted with turbine engines, increasing both her speed, and reliability. She was designed for 21 knots, and on her shakedown cruise sailed for 3400 miles at 17 knots without reducing speed for any reason. Her hull size and shape meant she was a stable gun platform, and could steam quickly in heavy seas. The engines also produced much less vibration than the earlier reciprocating engines, making her much more habitable for the crew. This increase in habitability was matched by a change in the location of the officers quarters. Previously, these had been in the stern, but in Dreadnought, were moved to the superstructure, closer to their battle stations. This might seem like a small change, but leads to a great increase in command efficiency. Her all-big-gun armament made fire control much easier, and vastly increased the range at which she could fight. In addition, she had a much heavier main armament - she could fire six 12 inch guns over bow or stern and eight broadside. A pre-dreadnought could fire just two forward or astern, and four broadside. She was fitted with an early form of director firing, and had better range-finding equipment than her predecessors. Her armour scheme was both thicker, and more effective. She had a thicker belt, and a better anti-torpedo bulge. Her turret armour was reduced, but this was because it was ineffective at protecting the turrets - concussive effects from a non-penetrating shell could reduce a turret's fighting capability just as much as if it had penetrated. Her watertight protection and compartmentalization was aimed at reducing the number of horizontal connections between compartments, greatly increasing her ability to survive flooding.

Had Dreadnought had to engage a force of her predecessors, she could simply have used her speed to remain at a favourable range, raining accurate, heavy fire on them. The pre-dreadnoughts would have struggled to reach the range at which they were most effective, and their armour would not have protected them from damage.

Sources:

Warrior to Dreadnought: Warship Design and Development 1860-1905, David K Brown, Seaforth, 2012

Dreadnought, Robert K Massie, Vintage, 2007

It was a combination of several things. But primarily it was her armament and speed.

Previews battleships might have 4 total 11in guns in 2 turrets fore and aft, then an 8 inch battery, a 5in battery, and some smaller ones.

By going all in on 10 12 inch guns Dreadnought could fire a greater weight of shells farther, and easier to spot as the guns all had the same range. She did retain a batter of light 12pdr guns for close defense.

And at 21 knots she was almost 3 knots faster than existing battleships, meaning she could chose the range, time, and positioning of any engagement, and flee if she needed too. This was accomplished by being almost 100ft longer then previous ships and using turbines as opposed to the previous triple expansion engines.

That meant she could from the get go, out range, out gun, and out run any existing battleship.

It should also be noted that other navies were on the same thought process, and the USN had actually designed their first all big gun ships before the Royal Navy but took much longer to build them.