Definition
Link building is the work of getting other websites to link to yours, so that search engines see your pages as recommended and rank them higher. Done well, it means creating something worth referencing and asking the right people to reference it. Done badly, it means buying links in bulk, which Google ignores at best and penalises at worst.
For a small business the best links are usually local and boring: the chamber of commerce, a supplier's partner page, a local paper, a trade body, a charity you sponsored. They are slower to get than a bought package and worth far more.
Short version: getting other sites to link to you, honestly or otherwise.