So as others have said, air is a poor conductor of electricity compared to water, and so you would need unrealistic levels of electricity to make this work.
Most super powers are essentially magic without the label.
Say you had a man with electric eel organs that could generate electricity. Coming into physical contact would transfer the electricity, but you might be able to project it with a little added technology.
There's a DARPA project I read about a while back that uses a laser to ionize the air into a plasma, which acts like a conductor for electricity. Eel man could get a hold of a hand held/wrist mounted laser and create a channel to send his electricity down, reducing the amount of current needed.
This may not be enough for a hard science approach, but it does get it a little closer.
If you don't like the laser idea, it could be a conductive whip instead, which would work very much like a taser; Flick the whip out, send a lot of volts through it.
Electricity needs a lot of volts to arc through plain dry air; roughly 3 million volts per meter. This is the amount of power needed to ionize the air to allow the arc to jump. After that it does get a little easier, but probably not enough.
An electric eel is around 2 meters long, and 4/5ths of that is the electricity generating organs. It has an output of around 600-800 volts and 1 amp for 2 milliseconds. In dry air that would arc around 3mm. With poor ionized air you'd be able to extend that a little, but not throwing bolts across the room.
A few researchers are working on making artificial electrical generating cells to power things like pace makers, and they suggest that the efficiency could be boosted, but aren't publishing numbers.
A few possibilities:
- Make it plausible and fun and no one will care that it's not hard sci-fi.
- Make it artificial, like a powered suit with batteries and capacitors and experimental tech.
- Give him some kind of biological capacitors that are slowly charged by the eel cells until there have enough voltage to do what you want.
- Use the whip idea. 800v/1a for 2ms isn't enough to kill anyone, but it would hurt just like a stun gun, and the range is whatever length the conductor is.