A vaccine contains a part of a germ (bacteria or virus) that is called an antigen. The antigen has already been killed or disabled before it's used to make the vaccine, so it can't make you sick. Antigens are substances, often a protein, that stimulate the body to produce an immune response to protect itself against attacks from future actual disease exposure.
In addition, vaccines contain other ingredients that make them safer and more effective, including preservatives, adjuvants, additives and residuals of the vaccine production process. Vaccines have reduced and, in some cases, eliminated many diseases that killed or severely disabled people just a few generations ago.
Vaccines, like any medication, are continually monitored for safety.