Even a question like this isn't so simple. There's at least a couple of ways electricity can hurt you. One is by interrupting the regular body regulation mechanisms, namely your heartbeat. Electricity passing across the heart can cause it to spasm. If it can't recover and find a regular heartbeat again you die. This is the most common way to get hurt and could happen from getting a shock from mains. The other is by electricity passing through you and burning you on the way through. This is common from lightning strikes as the electricity will pass through you to ground, rather than across the heart. It means you're less likely to die, but more likely to sustain injury.

In all cases, what hurts you is current. Current means electrons are flowing through you. As mentioned there are at least a couple of ways that current can affect you adversely. So it needs to be either a large enough current (so more electrons flowing), or a current going in the wrong place (across the heart).

So what makes current flow? Or, why do the electrons "want" to move? Voltage. A car battery has plenty of energy in it that could kill you in either of the two ways, but at 12V there's not enough voltage to get any current flowing through your body.

Voltage is the existence of an imbalance. Electrons "want" to be in a place where they are balanced with a positive charge. A battery represents a structure that is very imbalanced but the electrons are not able to move anywhere until the two ends of the battery are connected with a conductor. There are many ways that these imbalances arise but they are ultimately always the result of energy going in. When the imbalance is resolved the energy comes back out.

To hurt you a voltage also needs to be sustained long enough to pass enough current. A static shock is due to a very high voltage existing which it causes current to flow and why you can feel it, unlike the car battery. However, in an instant all the current has flowed and the voltage is gone.

So the answer is a high enough voltage and enough energy to sustain that voltage. Mains electricity can hurt you because it's high voltage (>50V) and can sustain that voltage all day long. Lightning can hurt you because it's very high voltage and can sustain it long enough (and that's only an instant) to cause serious injury.