A padstone is typically used to support the end of a beam (usually steel, but sometimes for timber beams too). The concentrated load from the beam is spread over a wider area of the masonry below to reduce pressure. Without the padstone, the induced load could be higher than the compressive resistance of the masonry, which could cause failure by crushing or cracking due to the stresses imparted into it.
I like to use the snowshoe analogy to explain this - if you stand on fresh snow wearing normal shoes, your weight would crush the snow and you would sink into it. Wearing snowshoes reduces the effect by spreading your weight over a wider area of snow, so there is less pressure. Another simple illustration would be to take some modelling clay and then push your fingers into it, which can be done very easily. But if you try to squash it with the palm of your hand, it is much harder.
As a side note, the same principle applies to foundations, which are usually wider than the wall they support, in order to spread the weight from the building over a wider area of subsoil. With softer soil or higher loads, the width of the foundation needs to be increased accordingly.
The required size of a padstone depends on the amount of load, the area of the beam which is bearing on the wall, and on the compressive strength (usually in N/mm2, where N = Newtons, which is a measurement of the force applied by the weight of an object due to (multiplied by) gravity) of both the padstone and the masonry below, the latter of which is factored to take account of aspects such as the mortar type and format of masonry units (eg standard bricks or blocks, or hollow blocks).
The padstone would clearly need to be of a higher strength than the wall below (as it would otherwise be pointless). The most common choices are engineering bricks, dense concrete blocks, and proprietary concrete padstones. Other options include concrete placed in situ, concrete lintels, or even steel spreader plates.
It is also worth noting that padstones are not always necessary. If the combination of loads and wall strength mean that the wall would not be over-stressed, then there is absolutely no point in using a padstone. In fact, maintaining uniformity in the material of the wall is usually beneficial as it reduces thermal bridging, as a dense concrete padstone is not as thermally efficient as the rest of the wall. It also potentially reduces the risk of cracking due to differential thermal movement.
Most importantly, follow the design/specification for each individual beam as this would have been calculated in accordance with the relevant design standard. Don't just buy an off-the-shelf padstone and assume that it will be sufficient for any beam on any wall.
Please feel free to comment below, or contact McAndrew Associates directly if you need any advice or assistance!