A common misconception is that hardwoods are hard and softwoods are soft. This is not surprising given the names and it is true for the majority of timbers, although there are many exceptions to this generalisation. The classic case is balsa wood which is actually a hardwood.
So how are timbers sorted into hardwoods and softwoods? It all comes down to the seeds. Hardwoods come from flowering trees with enclosed seeds (angiosperms) - so any fruit tree or tree with a nut or pulp around the seed is a hardwood. Softwoods come from trees with uncovered seeds (gymnosperms).
Hardwood trees tend to be deciduous, broad leafed, slower growing and more dense. Softwood trees are typically evergreen with needles instead of leaves, lighter in colour and in weight.
Wood hardness is typically measured using the Janka hardness test which measures the force required to push an 11.3mm metal sphere halfway into a timber surface.
Janka Hardness Test (http://www.precisebits.com/reference/relative_hardness_table.htm)
Eastern White Pine has a Janka hardness of just 1.7 kN (Balsa wood is 6 kN) while at the other end of the scale Australian Buloke (or Bull Oak) has a Janka hardness of 22.5 kN.
Bull Oak Tree (http://toowoombaplants2008.blogspot.com.au/2014/03/can-you-pick-mistletoe_23.html)
Having an idea of a timbers hardness is important when selecting wood for furniture. A tabletop made from pine is going to dint and scratch easily, whereas a bull oak top will last for centuries (just don't ask me to make it!).