Mesenchymal stem cells (MSCs) are isolated from multiple biological tissues—adult bone marrow and adipose tissues and neonatal tissues such as umbilical cord and placenta. In vitro, MSCs show biological features of extensive proliferation ability and multipotency. Moreover, MSCs have trophic, homing/migration and immunosuppression functions that have been demonstrated both in vitro and in vivo. A number of clinical trials are using MSCs for therapeutic interventions in severe degenerative and/or inflammatory diseases, including Crohn’s disease and graft-versus-host disease, alone or in combination with other drugs. MSCs are promising for therapeutic applications given the ease in obtaining them, their genetic stability, their poor immunogenicity and their curative properties for tissue repair and immunomodulation. The success of MSC therapy in degenerative and/or inflammatory diseases might depend on the robustness of the biological functions of MSCs, which should be linked to their therapeutic potency. Here, we outline the fundamental and advanced concepts of MSC biological features and underline the biological functions of MSCs in their basic and translational aspects in therapy for degenerative and/or inflammatory diseases.