The underlying mechanism of vaccination relies on the normal immune response of the individual receiving the vaccine. To oversimplify the many parts of the immune system, the antigen must be recognized by lymphocytes and cause B lymphocytes to proliferate and produce memory B cells. These memory B cells are what provide protection against future infection because they can be activated my quickly and easily. However, this does not always work in immunosuppressed individuals.

The extent to which a person is immunosuppressed can vary widely based on the cause. A few examples would be HIV, chemotherapy, or a variety of congenital immunodeficiencies. In general, it is important that vaccinations given to these individuals do not contain live virus or bacteria such as live attenuated injected vaccines. In these cases, the compromised immune system may be unable to clear even the small amount of weakened pathogen which is usually safe. The pathogen can replicate causing severe damage and even death.  

Other types of vaccinations, which do not contain live pathogen, do not carry this extreme risk because there is no replicating pathogen. However, this does not mean that the vaccination will be effective in activating the adaptive immune system. The effectiveness of a vaccine on an immunosuppressed individual depends on the nature of their immune suppression. If B or T lymphocytes are unable to function normally, vaccines may have a reduced or negligible ability to provide immunity against future infections. Overall, extra thought and caution should be used when considering the vaccination of immunosuppressed individuals.

http://www2a.cdc.gov/nip/isd/ycts/mod1/courses/genrec/11110.asp?seg=B