Lightning Projects contain all the artifacts related to your language design that are susceptible to depend on each others.
A Lightning Project is generally composed of Languages and of Language to Language transformations
How to create a Project ?
You can create a Lightning Project by simply browsing to File > New > Project... and by selecting the entry "Lightning Project" under the Lightning category.
Note that if the Lightning perspective is open, then one can directly choose the menu item File > New > Lightning Project in order to create a project.
Once the wizard appears, just give a name to the project. The name shouldn't be the one of an already existing project.
If your project does not appear in your package explorer, it might be due to the use of working sets.
Lightning projects are indeed not associated to any working sets upon creation. If you are using working sets, you will thus need to edit those latter so that it doesn't filter out your project.