Projects in Maya let you create a folder structure that contains all your scenes, textures, rendered images, etc.
How To Use Projects
Projects are a way of organizing files in Maya. Different files go to different sub-folders of a main project folder.
For example, let's say we're putting a scene together. We would put all our model textures in the source images folder and our scene files in the scene files folder. Now when we open Maya to search the textures, we would only need to put in "sourceimages\filename.map".
Creating A New Project In Maya
Step one - Go to file>project>new...
Step two - Set the name of the project; this will be the name of the project folder.
Step one - Go to file>project>edit current...
Changing The Current Project
Let's say you want to go back to a different projects folder. To do this, go to file>projects>set... Select the project folder (not the sub folders) and click ok.
Why Use Projects?
One advantage is organization. The next advantage, probably the most important advantage, is you can send a project folder to someone else's computer and all the textures and files will be sourced correctly. Because, instead of file locations saying "john doe/my documents/pictures/textures/example.map" it would say "souceimages/example.map". The problem with the first file location is, unless the computer you're sending it to also has the same file structure, the images will lose their connection with Maya.