Prestige dictates how famous and prestigious you are. Earning more prestige will increase your level of fame which will then provide more secular opinion (all except religious clergy). It will also give you a higher number of knights in your armies. To earn more prestige, you can go into the diplomacy lifestyle and select majesty focus which will give you another 1+ monthly prestige.
Your diplomacy skill affects this as well. Having a spouse with high diplomacy on the court politics task can help you here.
Your highest ranking title and all other titles will also affect how much prestige you earn. When you become a king or an emperor, you can expect to earn a lot more prestige.
If you’ve taken care of the gold situation, you can transfer some of that gold into prestige by organizing hunts and feasts. This will not only generate more prestige but also improve a lot of people’s opinion of you.
There are also quite a few relevant diplomacy perks that will generate more prestige so make sure to pick them all up.
Another good tactic is to create titles (if you have a lot of gold) and then give those titles to people that will make good vassals.
This is not something that you can do all the time because destroying titles costs prestige.
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