Golden shares are shares with extraordinary special powers, for example the right to block a takeover. The UK government holds golden shares in a number of privatised firms, e.g. BAE Systems and Rolls-Royce. So if you own shares in Rolls-Royce do not expect a takeover from a Russian oligarch with links to the Kremlin; the UK government will stop it.
Golden shares are also useful if a company wishes to preserve certain characteristics it possesses. Football clubs can have golden shares dictating, for example, that 80% of revenues from transfer fees be reinvested in new players (e.g. Nottingham Forest) – but Russian oligarchs are welcomed!