Shift/Brake Levers are also known as dual control levers. They have the ability of braking and changing gears in the same device. The most common style of shift/brake levers is to have the breaks accessible by squeezing your hand, with the gears being able to change by the movement of your thumb.
Road bikes shifters consist of a downward facing brake lever which when pulled activates the brakes. Shifting varies from brand to brand, however the common theme is that your hands don't need to move far from the brakes in order to actuate a shift.
Mountain bike shift/brake levers use a horizontal brake lever and a trigger gear changing system. This system is attached to flat handlebars and consists of three levers. Two are within a short distance of the rider’s thumbs or fingers, which when pressed changes the gears to a higher or lower gearing ratio depending on what is required and the remaining lever activates the brakes which is located within short finger reach. Note that due to the popularity of hydraulic disc brakes, this integrated shift/brake lever system is no longer as common as it once was.