I can't agree with post 3. Most of the world was already inhabited. European explorers were not discovering virgin wildernesses, they were encountering people, who lived in societies with histories of their own. Recent scholarly estimates have placed the number of people living in the Americas before contact with Columbus at somewhere close to 50 million people. West African states were well-established, wealthy, and powerful, which is one of the reasons that European explorers wanted to do business with them in the first place.
I think, along with the European domination described by Post 2, that the exchange of plants, animals, germs, and culture (often called the Columbian Exchange after Alfred Crosby's book of the same name) was the biggest effect. We often think of the spread of diseases as part of this exchange, and we should--the fact is that most of the 50 million people referenced above died within 100 years of 1492. But we should realize that crops and animals revolutionized the lives of people on both continents too. The contact also created, most scholars would agree, a network of communication, travel, and commerce between Europe, Africa and the Americas often called the Atlantic World.
The legacy of exploration was that most of the world became inhabited. I suppose it's up to you whether that is a good thing or a bad thing. People realized that they could find cheap or free land elsewhere, and many new countries were formed.
One part of the legacy is that the Europeans came to dominate the world. They explored and conquered essentially every part of the globe. This made Europe very strong and it also, you can argue, made the rest of the world weak in ways that continue to be felt today. You can say we're just getting out of the era of European domination with the rise of China, but it is still clear that European countries are generally much richer than countries in other parts of the world.