There are two common reasons preventing the removal of a resource from a project:

• The resource is assigned to one or more tasks. Replace those assignments with somebody else and you'll be able to remove the resource.
• The resource is the only project manager on the project. Make somebody else a project manager on that project and you can then remove them.

More information for manging resource in the project resource list can be seen in the following short video.
Create a Project - Adding Resources