Carbon is available in different forms. The best carbon is Highly Activated Carbon, then Activated Carbon, then plain Carbon, which is ok but not as good as the other 2 types.
Carbon adsorbs chemicals and heavy metals from air and water. In an aquarium it will remove plant fertilisers and medications from the water. It also removes hormones and pheromones produced by the fish. Carbon will also remove tannins from water, tannins are released by dead plants or wood that is soaking in water.
If there are lots of chemicals, tannins, etc in the water, the carbon can become full within a few days. If there isn't much to adsorb, it can last for a few weeks or even a month or more.
When carbon is full it does not adsorb any more. Under normal conditions the carbon will not release the stuff it has adsorbed. However, if there is a sudden change in temperature or water conditions, the carbon can release everything it has adsorbed and you can end up with a heap of chemicals in the tank water that poisons the fish and other inhabitants.
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Most companies that sell aquarium filters add a packet of carbon to the filter as a form of filtration media. It is a bit of a gimmick/ ploy to get you to keep buying products. Filter pads are the same thing. The better quality filters use sponges and ceramic beads, which last for years and don't need to be replaced every few weeks.
If your filter has a pad/ cartridge in it, buy some sponge for a different brand of filter and cut the sponge to fit in your filter. Put the sponge in the filter next to the pad and in a couple of months, throw the pad away and leave the sponge.
Filter sponges should be washed out in a bucket of tank water at least once a month and every 2 weeks is better. However, do not clean a filter during the first 6-8 weeks because you can wash out the beneficial filter bacteria and cause the tank to cycle again.
Tanks that are cycling usually have ammonia and nitrite levels that cause health issues to fish.