What does "Available to me" project mean?
When a client is happy with your work, he or she can add you to a pool of their favorite writers, called "My Team". This means you are likely to receive a lot more direct recurring orders from them in the future.
Projects that are assigned via My Team trigger a special email notification to you and are listed in the personally assigned projects in the available projects page. You still need to submit your pitch so the client knows that you understood the brief and the client actually likes your proposed ideas.