An asset is something you own that will earn you money in the future. In the real world assets are your brain, buildings and businesses. In the world of finance, assets are shares, bonds, cash, gold and other financial instruments and investments. Different types of assets (different asset classes) behave differently in different market conditions.
This is discussed in more detail in these posts:
Comparing ETFs: Asset classes
OUTstanding money: The beginner’s guide to investing
Podcast: Five concepts that will make you rich (rebroadcast)