The inertia force experienced by the roof is transferred to the ground via the columns, causing forces in columns. These forces generated in the columns can also be understood in another way. During earthquake shaking, the columns undergo relative movement between their ends.
In the figure above, this movement is shown as quantity u between the roof and the ground. But, given a free option, columns would like to come back to the straight vertical position, i.e. columns resist deformations. In the straight vertical position, the columns carry no horizontal earthquake force through them. But, when forced to bend, they develop internal forces. The larger is the horizontal displacement u between the top and bottom of the column, the larger this internal force in columns. Also, the stiffer the columns are (i.e. bigger is the column size), larger is the force. For this reason, these internal forces in the columns are called stiffness forces. In fact, the stiffness force in the columns is the column stiffness times the relative displacement between its ends