For about 75 years (1775-1850) European countries and their colonies experienced crisis after crisis in their governmental practices. The revolutionary ideas came from the philosophies of the Enlightenment, which held the radical concept that if you didn't like your government, you could change it. And change they did.
The American Revolt against England influenced the French Revolution; in the first case, the colonies successfully established their own country; in the second, the dispossessed within the mother country overthrew the government with only moderate success, but the pattern was established.
In the New World, what had happened in North America against Britain began to happen in South America against Spain -- the Spanish Empire, like the British, began to break apart. Meanwhile, in the Old World, the revolution in France inspired similar movements in what was to become Germany and Eastern Europe.
So Europe underwent its own political transformation, even as its colonies established themselves as independent countries.
After the French Revolution, revolutionary ideals like democracy, liberalism and nationalism came to be very powerful in Europe and in Latin America. These ideals sparked uprisings in many European countries and in almost all of Latin America.
There were so many revolutions/rebellions from the 1810s to the 1840s that you can't really say any one thing typifies them all. But here are some examples:
- Germany's 1848 revolution was about the desire for democracy and for a unified Germany (this shows the influence of all three ideals we mentioned).
- The Mexican wars of independence in the 1810s and '20s were driven largely by nationalism and the desire of the creoles to have soveriegnty over their homelands.
So these ideas were causing rebellions to occur in many different countries.