Shiny metal devices that hold falls and help you get up the rock. They're generally amassed over time and more specific pieces might never be required, depending on which discipline you fall for.
The link between you and your protection, carabiners have different shapes, different types of gates, and are designed for different climbing situations.
The function of a belay device is to provide friction so a belayer can catch and hold the weight of a climber who falls. Most devices are also used to rappel, or descend, from a climb.
Bolts are small permenant anchors drilled into the rock at regular intervals on a climb. Climbers attach the rope to the bolts using quickdraws as they ascend.
Active pro is used to protect trad climbs, and includes the stuff with moving parts: cams and tube chocks.
Passive pro includes the pieces on your rack that have no moving parts: nuts, tri cams, and hexes.
The strength ratings for climbing gear exist to give you clear and conservative information about the limitations of the equipment.
Climbing hardware will wear with time and can be damaged if dropped. Examine gear regularly and clean and lubricate moving parts to keep clips and triggers from sticking.