Vintage Computers - Filter Capacitors
NOTE: The following is a simplification, produced for high-level educational purposes.
ANALOGY
At your house, you consume water that is supplied by a water company. You require that water to be clean. Not 100% clean, but clean enough.
Although the water company filters the water at its source, in order to get to you, the water travels through pumps, pipes, junctions, etc. So, the water distribution network unintentionally introduces contaminates (dirt, etc.)
To cater for that, the water company places filters at various points in the water distribution network. You may even have a water filter somewhere in your house.
COMPUTER
The power distribution network in your computer is somewhat similar. As the voltage from the power supply travels about the consumer circuitry, voltage noise is introduced along the way. Certain capacitors in the circuitry (placed at strategic points) act as noise filters. This is why these capacitors are sometimes known by the function they are performing; 'filter capacitor'.
Sometimes, if a filter capacitor fails, the circuitry can 'get by' without it. It comes down to how noisy the area is where the filter capacitor resides, AND how tolerant the circuitry in the area is to noise.
For example, the filter capacitors that target dynamic RAM chips are crucial. If one or more of those fails, RAM operation can fail or become unreliable. (These capacitors are very close to the dynamic RAM chips.)
For example, on the IBM 5160 motherboard, the -12V line only feeds the ISA expansion card slots; no 5160 motherboard circuitry uses -12V. If I have no expansion cards that consume -12V, then the loss of the -12V filter capacitor on the motherboard will not impact on anything. And if I did have an expansion card that consumes -12V, then often, the designers of such cards put adequate filter capacitors onto their cards.
If you do not have the knowledge to make a valid decision about whether or not to replace a faulty noise filtering capacitor, then it's simple - fit a new capacitor.
ALIASES
Filter capacitor may also be referred to as 'decoupling' capacitor or 'bypass' capacitor. Filter capacitor is my preferred term here because I believe 'filter' better suits the analogy.
Of those, at the electronics school that I attended, for consistency, only 'bypass capacitor' was used. In the introductory subject of resistors/capacitors/inductors, it was explained that capacitors, at a simplistic level, can be thought of as passing AC and blocking DC. And therefore, when a capacitor was placed between a voltage rail and ground, in order to filter out noise (a form of AC), the capacitor was 'bypassing' the noise to ground.