The Agile Manifesto is a guideline how to collaborate in agile projects. The goal is to achieve better results by working together.
The Agile Manifesto defines four main rules on how to work together in a project:
Individuals and interactions over processes and tools
Working software over comprehensive documentation
Customer collaboration over contract negotiation
Responding to change over following a plan
Individuals and interactions: Talking to each other and meeting a colleagues or customers needs is more important than insisting on certain processes or tools.
Working software: The main goal is to have a working software. This must be the focus. A great documentation is nice but if the code is self-explaining, then the documentation is not that important anymore (a user documentation might be needed though). See Clean Code
Customer collaboration: Work together with your customer and try to meet his or her wishes. This leads to a way better result and a more satisfied customer than negotiating every little detail in a contract.
Responding to change: Requirements change all the time. Try to adapt to the changes. This leads to a better software and higher customer satisfaction.
The Agile Manifesto also defines Twelve Principles of Agile Software which can be found on their website.