The current is basically a description of charge movement or change. The same movement of charge that in human body can polarise and depolarase tissue, where the most significant change happens when polarising the hart between its nods. A big enough change in this behaviour will make the hart movement irregular. The value of 250 mA AC, or a bit more for DC, is enough to kill a person.

The voltage is a difference between potential. This means that with high enouge potential the voltage can still be small dependig on the difference. When there is a difference in voltage between two points connected with some resistance there will be a movement of charge, or current. This current is only significant if the value of resistance is small enough as I = V / R, where I is the current, V is the voltage, and R is resistance.

You can see an exploit of this when someone says he will endure milions of volts for a long period of time as a stunt. The fact is that the current he is experiencing is too low to do any damage, lowered by some kind of resistance.