Nationalism is a modifier that applies to all conquered provinces once conquered.
What does it do?
In Europa Universalis IV, every province in your country has a "most likely" rebel type if the revolt risk in the province is above 0, you can see what type by hovering the mouse over the revolt risk window and reading the tool-tip.
These rebel factions will surface at a percentage chance per month according to their revolt risk.
Once conquered a province gets +14.00 revolt risk from Nationalism.
How long does this last?
Nationalism last for 10 years after being conquered, as the tool-tip states
Well, apart from giving an increased revolt risk by virtue of being affected by nationalism. Not much, it just makes it increasing likely that you will suffer the spawning of a nationalist rebel stack/army.
Is this bad or good?
Well, rebels are annoying, Nationalist rebels have a few specific goals, and they can achieve those by successfully negotiating demands from their overlords when they control at least one province.
Nationalist rebels scoring a victory by their overlord negotiating therefore confers the following penalties and benefits titled local autonomy:
The one advantage of allowing the rebels to succeed in their war goal, at least to the point of negotiation is that you gain
to the province, which may help you maintain order in your empire if at a particularly low stability or prestige/weak geo-political standpoint.
If you let them enforce their demands however, by letting the war-score tick over and not dealing with the irritating rebellion, you will find yourself acquiescing to the nationalistic rebel's demands, which has the following effect: