For general advice on Graduate School, see the department’s Grad School webpages. Much of that advice is generally relevant; here we speak to the specifics of the Master of Fine Arts, the M.F.A.
An M.F.A. offers you time to write (usually for two years) and have your work critiqued by other talented young writers as well as by the established writers on the faculty of the program. It also trains you in the critiquing of others’ writing, a training that you will ultimately apply to your own work. Coupled with significant publication and some teaching experience, the M.F.A. also gives you an academic credential that allows you to apply for an academic teaching job.
But be warned: If the job market for literature Ph.D.s is grim, the market for those with M.F.A.s in creative writing is perhaps even worse. The M.F.A. is not a professional or vocational degree, nor is there a job waiting for you out in the world as a “Writer.” But the discipline of a quality program will likely enhance the likelihood of your becoming a published writer.