STI is an acronym for Sexually Transmitted Infections, formally known as STDs, or Sexually Transmitted Disease (the argument for the switch is that not all sexually transmitted symptoms are diseases, but they are all infections). Although they can be contracted by coming into contact with infected bodily fluids, such as blood, semen and vaginal secretions, many STIs, such as herpes, can be transmitted in any activity that requires coming in contact with any infected mucous membrane.
Contracting an STI in a body modification procedure itself is almost unheard of, when done by a professional artist who uses gloves, autoclaved tools, and uses disposable needles. In body modification, STIs are most commonly transmitted through sex with fresh genital piercings. While it's generally not a good idea to have sex with a fresh body modification, the risk of exchanging an STI with your partner(s) is greatly reduced with a condom.
While some STIs have little effect on the body modifications themselves, they can put a severe damper on your sex life and pose a serious health risk if left undetected.