Inertial mass $$m_\text{t}$$ is the constant of proportionality in Newton's second law of motion: $$F~=~m_\text{t} \, a$$. Inertial mass provides resistance to the change in the state of motion of a body. The state of motion changes when the direction or acceleration of the body changes. Gravitational mass $$m_\text{s}$$ refers to gravity and influences how strong the gravitational force $$F_\text{g} ~=~ m_\text{s} \, g$$ is. Here $$g$$ is the gravitational acceleration.
Experiments have shown that inertial mass $$m_\text{t}$$ and gravitational mass $$m_\text{s}$$ agree to an accuracy of $$10^{-13}$$ and are thus assumed to be equal: $$m_\text{t} = m_\text{s}$$.