Looking at the image to the right, the regular or left sofa has the fabric pattern running up the roll and that is the normal way fabric is milled. The pattern or in the case of a velvet, the grain, would run up/down. The sofa on the right has fabric that is milled "railroaded", this means that the fabric is woven so that the pattern or grain is situated so that the top would be from one side of the fabric to the other side.
So why do this? There are times when the common 54" or 60" width of fabric is not enough to run the span of a piece of furniture. For instance if you have a very long cushion that exceeds the width of the fabric,(because you orientate the top of the pattern to the back of the cushion) instead of putting in a seam or two you could just find a railroaded pattern and you could run right across with no seams. The same would apply to sofa backs etc. Sometimes it is more efficient to cut fabric that is railroaded even if you don't have a large span because the pattern may be unusual and difficult to match.
Some fabrics can be railroaded even if they are not specifically woven that way. A plain tweed, cotton, vinyl and of course leather may not have an "up" or "down". In the case of vinyl or leather it does not matter which way you use it unless it has a pattern. Even if a fabric has a pattern it may be able to be railroaded, it depends on the fabric. For instance a geometric "square" or "diamond" could be situated regular or railroaded, you have to have a look in each direction and see if the look changes in some way. Chenilles and velvet usually cannot just be turned sideways as a makeshift railroading, however allot of chenilles and velvet do come railroaded for this very reason.
Most of the time you probably don't need a railroaded fabric, but when you do, know that is available!