From the standpoint of protection the most important value is lightning current because it is passing through the hit object. That current is not constant. It increases rapidly till the largest (peak) value. The time between the beginning of this appearance and the peak current value is called forehead of lightning.
The negative lightning hit produces current waves that can be relatively different. During the first negative discharge the length of forehead is equal 10-15 Ms. With the next discharge (if exists) the duration of forehead becomes shorter. The peak value of current is smaller than in first discharge.
The positive lightning hits are usually made of one discharge which has duration 0,1-0,2 s. The duration of forehead is relatively long and it's value is somewhere between 20 and 50 ms and peak value of positive current can grow even larger than 1000 kA.

PEAK VALUE OF LIGHTNING CURRENT
Peak value of lightning current is the most important value, because with it we can calculate the drop of voltage that it makes passing through some object on the earth: U=I*R. Because of that it is important for calculating the protection from lightning strike. Of course we don't know in advance what value of current we can expect so we can't construct the protection. However we know the possibility of appearance of certain current of lightning and that information we can use in calculating the protection. More about that in chapter Probability of lightning strike.

STEP OF THE LIGHTNING CURRENT
Steep of the lightning current is actually the speed of achieving peak value of lightning current. We calculate it by dividing the peak value of current with duration of wave forehead. It is important to us because these sudden changes of current in their nearness create changeable magnetic field. The value of voltage that is induced on objects in that field directly depends on the speed of variation of magnetic field.
Briefly: the greater the steeps of lightning current the grater are voltages and current values on objects close to discharge, and they even don't have to be directly hit by lightning strike. If voltage and electric current do not damage those objects, electromagnetic forces that are inducted by passing current still can damage them (If electric current passes through two conductors, a force is created among them. Direction of force depends on direction of electric current and its value depends on value of electric current and the distance between conductors.)
During the calculation of lightning rod protection we have to think about forces effecting the lightning rod. If they are too strong they could damage lightning rod itself.

CHARGE OF LIGHTNING CURRENT
Charge of lightning current is the charge that is neutralized during one strike. By itself that isn't so interesting information, but whole energy freed during the strike depends on it. On that energy depends melting of lightning rod or part of aluminum plate of plane.
That energy can be calculated as multiplication of charge and cathode voltage drop: W=Q*U

SQUARE IMPULSE OF LIGHTNING CURRENT
That is a value that is magisterial for calculating the heating of lightning rod installation, which conducts the current of lightning. By definition it is calculated by formula:

where "R" is the resistance of conductor, "i" is the value of lightning current and "t" is the time.