How could tesla or anybody else light up a light just by holding it

The ordinary light bulb that we use in everyday life is either LED (containds small light emiting diods) or it contains a wire that is heated to a high temperature and as a result light is produced.

For his demonstrations Tesla used bulbs that did not contain any part inside. Instead of any part there was a gas inside. These type of bulbs are still used. Their main advantage is that they do not require much energy to produce light.

Inside his light-bulbs Tesla and others put a noble gas such as neon, xenon and argon. Also, sometimes there was a phosphorus on the outside part of a light-bulb. When this light-bulb is brought into electromagnetic field it produces light. This happens due to foto-electric induction. When gas is positioned inside EM field gas gets exited. This causes for electrons to jump out of their positions and emit light. This can be achieved wirelesly as long as EM field is strong enough. 

Iwould say a is accurate