Resume, or Curriculum Vitae (C.V.), is a list of your education, work experience, teaching experience, exhibitions, collections, commissions, and other accomplishments (including a list of any important articles printed about your work, media coverage you have received, galleries or agents who represent you, and any organizations you belong to). It should list most recent activity first.
Artist Statement talks about what motivates you creatively and maybe what your philosophy of life is, or who you are. Why you do what you do, why you choose to work in a particular medium and style, and what ideas, feelings, issues or concerns you are attempting to express in your work. You can talk about your inspiration (personal heritage, loves, hobbies, philosophy, emotions, color...). You can write why you make things you do, what challenges you to continue making them, and what you hope to accomplish by making them. Artist statement is an insight into your creative process. Sometimes we do not even know what propels us to do what comes as a finished piece of art. Even that can be part of a statement.
Artists Biography is an overview of you and your work. It is generally a summary or highlights drawn from your C.V. and Artist Statement.
Portfolio is all three things above plus much more. It should include photos, slides, any press clippings or articles about you and your work, posters, invitations to solo exhibitions, etc.
All of these must be regularly updated.