In the absence of other interactions, we observe that things fall at a rate of 9.8 m/s/s. There's some flexibility in this number, but it's pretty close to this value everywhere on earth.
It's special we call it 'g'
This empirical fact means that the momentum principle predicts the force this object experiences is equal to mg.
This also turns out to be true. The force due to the Earth on any system near the surface of the earth is given by m_sys*g.
For example, tossing a puppy? m_puppy*g is the force of gravity on the puppy it is directed “downward” towards Earth's surface, so as a vector we often say is <0,-mg,0>.
When we can neglect other interactions our constant force equations give us a set of equations that govern the motion of systems experience local gravity.
Use CF equations to produce kinematic equations.
These are often useful when the only important interaction is the gravitational force.