Bong Sliders (AKA pull slides, sliding bowls and slider downtubes) are the stem/tube piece of "slider bongs" systems, they are at the base and stick out of the chamber at an angle higher than the water level. Bong slides have special marijuana smoking bowls attached to them and enables the user to control the air intake and the smoke that pass through the water when in use by using a sliding motion.
Normally in a regular "carburator bongs" when you inhale, the smoke fills the bong chamber while you block the little carb hole on the side with a finger, to clear the chamber you simply remove the finger blocking the carb hole while continuing to inhale, fresh air will come in from the hole instead of from the bowl to replace the smoke. With bong sliders however, it is a bit different... First there are no carb holes, so to clear the smoke, instead, slide bongs use glass bowls that slide in and out of the bong, the glass bowl from bong sliders have a little handle attached to them, so in order to clear the chamber all you have do is grab that little handle and lift up (aka slide it) the slider while inhaling.
If you broke your existing slide and you need to replace it, then you should get a good quality replacement bong slide that will not break easely ( unlike your previous one ) The good bong glass sliders will usually cost 15$ to 30$, this is a good investment, you can go with the more fancy and colorfull versions if you have more money aswell. All the bong slides pictured above have bowls with double glass walls for extra heat resistance.
In general if you have a medium to small glass slider bong, the 9mm Bong Slides will fit most likely fit your standard size glass bongs, most non name-brand bongs usually have 9mm slides. The 9mm mesure is the diameter of the bowl, if you want something bigger then there are bigger bowls suchs as the 12mm and the 15mm. Be sure to measure your glass bong's stem before you buy or else just be safe and get the 9mm...