"Major powers" is a term used to describe countries which are given great advantages in the game, so that they tend to become the largest and most powerful countries in most games. The major powers of a particular era tend to be those countries which are selectable at the scenario start. These nations are mostly the most interesting, most powerful or soon-to-be powerful countries.
There are several kinds of advantages that countries can have. The major powers will tend to have all of these.
Many countries have some pretty large advantages simply for being them, encoding in their scripted events files. For example, several countries get a shipyard given to them by event, regardless of their naval tech levels. Many countries get free, no-fail religious conversions.
Another kind of event with a huge impact on play, especially for AIs, is inheritance events. There are not many of these, but they can easily double the size of an AI country. Austria is the best example here; it rarely fails to become a major power in any game because of its inheritances of Burgundy, Hungary, and Bohemia.
Cores, Culture, Wealth, and Religion
A country with many core provinces gets many advantages, because core provinces generate more taxes and manpower, don't rebel as much, and cost no BB to take in war. Also, for the AIs cores guide them in terms of going to war in a more or less sensible way.
Another big advantage that all major powers have, is having a large area of acceptable culture. For example, there are 27 provinces with French culture in the 1419 scenario.
Sitting on wealthy provinces, rather than poor ones, is another large advantage. For example, the average base tax value of the 27 French provinces is 9. Their average manpower is 5.
Finally, it is advantageous to start with a unified country religiously, and also to have a wide area of state religion to expand into.
A single leader, controlled by a human, can make a huge difference in war. With allies, he can steal sieges. By himself, he can command every battle of substance and thus leverage his shock or fire stat to the utmost. AIs tend to be helped much less by leaders since they don't know how to exploit them, but they can still make a difference. And this is especially true if the leaderfile is deep enough that most of an AI's armies are commanded by a leader who is better than average.
Conquistadors and Explorers
Most countries do not get any leaders of any kind, much less any explorers and conquistadors. All countries can get a random conquistador, but he usually won't be very useful without sea access to unknown lands. Getting a random explorer in time to compete with Portugal and Spain is very hard. Without the ability to explore, these countries must therefore either get maps from Portugal and Spain (hard, and very unlikely for the AI), or give up on the riches of the colonization game.
By contrast, Portugal, Spain, France, England and the Netherlands get large numbers of excellent explorers and conquistadors.
Some of the AI files are better than others in some ways. However, there is one way that stands out: most AIs never, ever, colonize, even empty provinces right next to them.