Brass is a particularly commonly used metal when it comes to the materials used to construct saws. If you are cutting through a relatively soft object, such as wood, then a saw with brass construction will do just fine in that case. Brass is a popular choice of blade because it is a cheap material. Brass is also a fairly convenient material to work with, as it melts at a lower temperature than other materials used in saws. This makes brass blades a fairly common choice when it comes to saw materials.
When working with a saw made of brass, you are most commonly going to see the backsaw in action. The backsaw includes any saw used by hand that also has a stiffening edge opposite the cutting edge. Backsaws typically have a thin blade, but also cut straight and without wobbling as you work. To achieve this stability, backsaws usually have an edge along the top that is made out of a relatively sturdy material. This top edge will allow the blade to be both thin and rigid.
The top edge that you are going to see is commonly made out of brass. Brass is cheap to use for this purpose and will usually provide the rigidity required for a backsaw. Backsaws are most commonly used for work where a reasonable amount of precision is going to be required, such as in cabinetry and joinery work. To get the precise cut that is needed, backsaws usually have close set teeth.
Backsaws can range from the most basic and affordable models to those that are of the highest quality. The Lie-Nielsen Independence Backsaws are a great example of backsaws that put the focus on the highest levels of construction quality. The Lie-Nielsen backsaws are modeled after the classic Sheffield saws seen in the 1830s. One of these, however, will run you about $139. Most backsaws are a great deal more affordable. Woodcraft makes backsaws for around $9 that are very much suitable for most everyday work.
Brass is a great choice for a wide variety of jobs, but there are some circumstances under which brass simply will not suffice. Anything of a consistency harder than wood is likely to damage a brass saw. For jobs involving anything hard such as rock or concrete, a diamond saw would be much more suitable.