Adam Rice's answer is correct, but this just adds some clarification.
You have cable-actuated disc brakes, as stated elsewhere. Higher end bikes have hydraulic disc brakes, where hydraulic fluid pumped through a hose moves the brake pistons (the things inside the brake that push the pads onto the rim). This is the same mechanism that cars use. Another alternative, especially on older bikes, is rim brakes, where the cables will pull calipers shut. On all types of brake, the pads wear out with use.
On only rim and cable-actuated disc brakes, as the pads wear out, you have to adjust the brake cable tension. (On hydraulic disc brakes, the pads self-adjust.) Say the pads started out at 2mm thick, and you wore them down to 0.5mm (per the dealer manual that Adam linked, those dimensions are actually the starting thickness and minimum usable thickness, i.e. the pads are now worn out; see diagram on page 4). The cable now has to pull the pads 1.5mm further in towards the rotor (or rim) before they start to bite. Hence, you need to tighten the cable. On caliper rim brakes like older road bikes use, you just need to tighten one cable adjuster and both pads move closer to the rim. On cable actuated disc brakes, you need to tighten two adjusters, one for the outboard pad and one for the inboard pad. The red arrow below shows the bolt to adjust the outboard pad.
There should be a barrel adjuster elsewhere on your bike to move the inboard pad closer to the rotor. There doesn't appear to be a barrel adjuster on your brake caliper, so I would look either at your brake lever (if you have flat bars) or follow the cables to the downtube of the frame if you have drop handlebars.
As I stated in comments, the brake calipers are the big metal things that the cables connect to. The pads can be removed from the caliper. You pull out the cotter pin, shown by the blue arrow, to access the pads. If you liken the brakes to a printer, then the pads are like the printer's ink or toner cartridges, and they can be replaced separately from the parent item. When we say "brakes", we usually mean the brake calipers. Now, bikes may not have internal combustion engines, but they do have a lot of discrete parts, so new cyclists might commonly use an over-general term, e.g. say "wheel" when they mean the rim or the tire. This is understandable, and you get used to the terminology with time. In any case, as stated elsewhere, if you were not adjusting the cable tension, you were throwing pads with useful life away. I would assume from the rust on the calipers that you didn't replace the calipers wholesale, but this would also be unnecessary. I think you would have to ride very consistently in harsh conditions to see a several month replacement cycle on pads. Below is a photo of worn out brake pads from Total Women's Cycling: