Something big is just plain large or important. A big class has a lot of kids. A big room is larger than average. A big newspaper story is one that makes the front page.
Some people hate the idea of "big government" which means a federal government that plays a significant role in the day-to-day lives of its people. You might talk big at your reunion, but you really haven't traveled the world. (You went to Hoboken and Walla Walla!) Big can also pertain to age, as in "Will you be a big girl and get dressed all by yourself?"