Hardwood is not necessarily a harder material (more dense) and a softwood is not necessarily a softer material (less dense).
Different types of construction projects call for different kinds of timber, both hardwood and softwood are used for everything from structural to decorative.
Softwood and hardwood are distinguished botanically in terms of their reproduction, not by their end use or appearance. All trees reproduce by producing seeds, but the seed structure varies.
Softwood trees are known as a gymnosperm. They reproduce by forming cones which emit pollen to be spread by the wind to other trees. Pollinated trees form naked seeds which are dropped to the ground or borne on the wind so that new trees can grow elsewhere.
A hardwood is an angiosperm. Angiosperms usually form flowers to reproduce. Birds and insects attracted to the flowers carry the pollen to other trees and when fertilized the trees form fruits or nuts and seeds.
The hardwood/softwood terminology does make some sense. Evergreens do tend to be less dense than deciduous trees, and therefore easier to cut, while most hardwoods tend to be more dense, and therefore sturdier. In practical terms, this denseness also means that the wood will split if you pound a nail into it. Thus you need to drill screw or bolt holes to fasten hardwood together. But structural lumber is soft and light, accepts nails easily without splitting and thus is great for general construction.
To sum up
Hardwood tend to be darker, heavier, more expensive, last several decades, naturally resistant to weather.
Softwood tend to be lighter in color, lighter weight, cheaper, last for a decade or so and can be weather resistant but needs to be treated.