Mob rule is sometimes called ochlocracy or mobocracy. There is sometimes no legal government, and mobs of people decide whatever they want. It is government by a mob (crowd of people). In this system, the mob becomes the ruler or dominant force in society. Actually, it is rare for a whole country to be under mob rule. More frequent is for part of the country to overthrow its leaders and be for a time without a government. Parts of a country may try to secede (break off) from the country. That has been quite common in certain parts of the world.
Mobs do have leaders, who make speeches complaining about what is wrong, and what they want instead of the legal government. Sometimes mods succeed in taking over the whole country (Russian revolution), sometimes they fail because the government succeeds in using force to stop them. The British decision to ban the trade of slaves (William Wilberforce) was fiercely resisted by the people who made money out of the trade. Slave trade mobs attacked the homes of people known to support abolition.