Speaker's Corner is the place where people speak up their mind to a "willing audience". Contrary to popular belief there is no statutory basis for the right to speak at Speakers' Corner. It is just "tolerated" and a tradition now. Even a tourism attraction.
The history of this Speakers' Corner starts in 1855. Public riots broke out in the park about the "Sunday Trading Bill" which forbade buying and selling on a Sunday. The park was used by the movement as a point of assembly for workers' protests. They forced the "right to speak" in Hyde Park. That resulted in the "The Parks Regulation Act of 1872". It allowed "public meetings".
These riots were described by Karl Marx as the beginning of the English revolution.
A lot of people think this is the only Speakers' Corner in London, but that is not the case. There are Speakers' Corners in Finsbury Park, Clapham Common, Kennington Park and Victoria Park. But this one here is definitely the most popular one.