A project is something you're working on for a client or internally. Typically a project is created automatically from the Sales pipeline by Winning a Deal, but you can also create a project manually.
There are two main types of projects: Client and Internal. Client projects are the ones you do for your clients (and that you'll eventually charge for), while Internal projects are the ones you do for yourself.
A project has a couple of main parts, and we'll explain them briefly here:
(1) project members - people who do the work
(2) tasks - describe what needs to be done
(3) notes - a knowledge base for your project
(4) financials - tell you how much money a client is spending (and if he is profitable for you)
(5) time entries - see how many hours people spend on this project
(6) invoices - keep track of sent and paid invoices
(7) activity - this is like a news feed for you project. Everything that happened on the project is right there, sorted chronologically.
Since Internal projects don't have any revenue, they don't have the invoicing section available.