The bearing is the part that allows the drum to spin freely with minimal friction. The bearing has an outer shell that protects it and keeps it in place through friction.
The outer shell of the bearings is encapsulated in the drum shell to keep the outer shell in position (so that the shaft doesn't slide out).
If you look around the bearings themselves, you'll notice a large metal piece. The purpose of this metal is to firmly attach the bearings to the drum shell so that it remains stable, and that is why there are several holes around the part. The majority of this piece is encapsulated inside of the drum shell to make it even more stable, and the shape of it helps with this. This metal piece is made from cast aluminum, as it should be lightweight yet strong.
The process used to manufacture this part of the machine is likely via die casting, due to the apparent lack of giveaway markings such as break-off points where the sprue of the mold would be in normal casting.
Aluminum is a lightweight yet comparatively strong material. This lightness is one of the reasons why aluminum is valued in these kinds of driving systems, as it reduces the total weight of the rotating components, allowing for more energy efficiency. Aluminum is also corrosion resistant and more importantly, resistant to oxidization. Aluminum reacts with oxygen to form a hard film of aluminum oxide that prevents further oxidization.
A video on the manufacturing process of aluminum can be seen below.
The bearings themselves, unlike the metal that keeps them in place, must be free to move within their constrained area so as to allow the shaft to spin smoothly, and they must be made from a hard material so as to make sure it continues to spin freely. Stainless steel works for this, as it doesn't corrode and is very hard, meaning it will continue to work properly and let the shaft move freely for a fairly long time.
The ball bearings are made by being cut from steel wire and rounded off to form the perfect ball shape necessary for them to function properly in various applications, in this case, the washing machine.
Stainless steel is a specific variant of the steel alloy, consisting of at least 11% chromium in order to protect against corrosion (rusting). Chromium works similarly to aluminum, in that it forms a thin layer of chromium oxide on the surface of the object so that the steel alloy under it is unable to react with oxygen and oxidize. Compared to aluminum, stainless steel is stronger, at the cost of increased weight. However, unlike aluminum, which softens at high temperatures and conducts electricity well, stainless steel does not.
A video on the manufacturing process of ball bearings can be seen below.