Furnace filters have an arrow that point to installation towards the evaporator coil, fan and blower motor located inside the air handler. If there are no arrows on the filter, install the filter with the sturdiest side as the back.
When installing any type of filter, look at the filter to determine the denser side. Some filters have a cardboard or mesh face on one side that indicate a sturdier design, so the filter would be installed with the less sturdier side facing towards the air flow so it filters through that side first.
If the air filter is not installed correctly, it could impact the air flow in a very negative way. Within a couple of weeks dust and other debris will accumulate and not only impact the life of the furnace motor, but also drastically reduce the efficiency.
Installing a furnace filter requires proper direction, but with some media pad filters there is no difference in what direction is used to install the filter, but pleated filters must be installed in a specific way in order to work properly. The reason it is so important to have the air filters installed facing the right direction is due to the fact they are designed to work best with a specific direction of air flow.