advance
To move forward or make progress toward a goal.
Advance means to move forward or make progress. When an army advances, it moves toward its objective. When you advance to the next grade, you're moving forward in school. A scientist who makes an advance in cancer research has moved the field forward with a new discovery.
The word carries a sense of purpose and improvement. When you advance, you move forward with a specific goal in mind. A chess player who advances her knight is moving it strategically across the board. A student who advances in math has genuinely learned more and can solve harder problems.
Advance can also mean to happen earlier than expected. If you get an advance copy of a book, you receive it before the official release date. Teachers sometimes give advance notice of a test so students have time to prepare.
As a noun, an advance means progress itself: medical advances have helped people live longer, healthier lives. The word also refers to money paid before it's due. An author might receive an advance on a book before writing it, which she'll earn back through later sales.
The opposite of advance is retreat or fall back. When you advance, you're moving confidently toward something better, whether that's knowledge, position, or achievement.