A bodyguard is someone who protects another person from harm. Typically such protection is against physical harm such as assault or even murder. Such a role can be part of the duties of members of police or military agencies, or be a private arrangement between two parties.
Gral seemingly offered to act as the bodyguard of Quark while briefly serving as Grand Nagus in 2369. He offered to protect Quark from those who were "jealous" of his position while simultaneously threatening him harm if he did not receive lucrative Gamma Quadrant business opportunities. After that, Quark asked Rom to be his bodyguard. (DS9: "The Nagus")
Benjamin Sisko provided bodyguards to Li Nalas in 2370 when the Alliance for Global Unity was threatening the Bajoran Provisional Government. Sisko feared that Li's status as a hero would make him a target of the Alliance. While Li felt such protection was unnecessary, Sisko provided it nevertheless. (DS9: "The Circle")