Buffering capacity (also called alkalinity) is the measure of water's ability to absorb acid without dropping in pH. Biological processes - such as decomposing waste matter - create acids, and as these are produced in the aquarium they react with the water's buffering agents and are neutralised so the pH remains constant. If insufficient buffering agents are present however then they quickly become saturated with acid and the pH begins to drop.
Water's main buffering agents are the dissolved salts and minerals which make up water 'hardness', the GH and especially the KH. Hard water, which contains a lot of dissolved minerals and salts, generally has a high buffering capacity and tends to be neutral to alkaline. (My water for instance has a KH over 300 and a pH of 8 - 8.2). Soft water contains far less salts and minerals - i.e. less buffering capacity - and tends to be acid to neutral.
There is a big difference between pH agents and buffering agents. 'pH Up' or 'Proper pH' are pH changing agents: they will make the water more acidic or more alkaline. However, they don't actually buffer the water; you either need a commercial buffering agent or something like baking soda or oyster shell to do that. You need to raise the KH, not the pH, in other words, to hold pH at a steady level if your water lacks hardness.
Two scenarios:
1. The tank has soft acid water but the owner wants it to be neutral to alkaline, so adds pH raising agents. The pH will rise, but in the presence of inadequate buffering capacity (not enough dissolved salts) the metabolic processes in the tank soon produce enough acid to neutralise the agent and drop the pH back down. At the next water change more pH agent is added to boost the pH, so up it goes... and back down again. This rollercoaster ride is highly dangerous to fish.
2. The tank has hard alkaline water but the owner wants it to be soft and acidic (e.g. for rainforest species). So pH lowering agents are added, but because these do nothing to remove the minerals which make the original tap water hard and well-buffered, the agent is quickly neutralised by the water's natural buffering capacity, so the pH dips and rises sharply. The owner adds more and more pH Down to try and stop the pH rising, but because their water already contained a lot of salts, and the neutralisation process produces more salts, they end up with tank water which is chemically not much different from pickling brine, plus a rollercoastering pH level! Bye bye fish.
If you want to bring your pH up to a certain level therefore, you need to make sure the water is well-buffered first (use a commercial buffer or oyster shell / baking soda to add 'hardness'). These products will bring the pH up at the same time as the buffering capacity - remember the harder water is, the more alkaline it tends to be - and will keep it stable.
If you want to bring your pH down to a certain level however, you need to physically remove substances from it, not add more. Peat moss in the filter is one way (it removes some of the dissolved minerals and adds acid) and mixing tap water with RO water or rainwater are others.
Hope this helps.