Just happened across this yesterday when randomly walking across Hyde Park (because the Circle Line was down and District Line closed between High Street Kensington and Edgware Road leaving no sensible way of getting from Chiswick to Lancaster Gate on the tube, grumble grumble). It's to commemorate a tree which was burned down in the Reform Riots of 1866, the stump of which then became a noticeboard for political demonstrations (all from the Press Factsheet on the Royal Parks website). Apparently a new tree was planted in 1977 but I couldn't tell if that had since gone or if this monument was not actually on the site of the tree.
My historical knowledge being appalling I didn't know about the Reform Riots but here's some info from the National Archive website:
Following the 1832 Reform Act, periodic demands for the extension of the right to vote continued. Further attempts at parliamentary reform took place in the 1860s. By 1865, both Liberal and Conservative leaders, William Gladstone and Benjamin Disraeli, were convinced of the case to extend voting rights. In 1866 reform demonstrations turned to riots in Hyde Park and Trafalgar Square. The Reform Acts of 1867 and 1884 extend parliamentary voting rights: firstly in 1867 to the urban adult male householders and male lodgers paying £10 for unfurnished rooms, and secondly in 1884 to men living in the countryside (under the same conditions).