You just bought a company, and then you find out that a key piece of code doesn’t below to your new business (e.g. see the Skype lawsuits). Representations, Warranties & indemnities are the contractual tools that buyers and sellers use in M&A (Mergers and Acquisitions) to derisk these situations.
In the US, the terms representations and warranties are used almost interchangeably. Under English law there are strong differences. A warranty is a promise that a statement is true, so breaching warranty usually gives rise to claims for breach of contract. A representation in M&A means you can be liable for misrepresentation, which has potentially much higher costs.
Here’s a great introduction from a US firm: http://hyndmanlaw.com/blog/ma-issues-reps-warranties-indemnities-part-i/
And here’s detailed coverage of the difference between representations and warranties from from UK firm