Earning the right to ride in the front passenger seat of someone's car. This is also the direct opposite of "riding bitch," where you are sitting center-backseat, sandwiched by your friends (aka: riding gay, riding whore). It is "shotgun"'s responsibility for controlling car temperature, changing radio stations, calling out landmarks, and flagging down hot girls.
Variations to "calling shotgun" can include paper/rock/scisors, coin flip, or being the first to yell "shotgun" when the driver pulls their car keys out of their pocket. Seniority rarely means anything when calling shotgun.
Steve was riding shotgun because he won the coin flip in the mall.