Thymus dependent-Have peptide components which can be presented to T cells for via MHC for a response.
Thymus independent-Have non-peptide components which cannot be presented to T cells via MHC for a response.
Good examples of thymus independent antigens are the polysacharrides coating the SHiN organisms. You need antibodies or C3b to coat these organisms so that they can be destroyed via MAC, phagocytosis, etc.
A clinical scenario for the thymus dependent antigens could involve anything that impairs T cell response (e.g. DiGeorge) or the presenation of protein antigens to T cells.