Burning (=oxidizing with oxygen from the air) organic material generates heat, because the reaction is exothermic, CO2 and H2O being energetically more stable than the organic material before combustion. Of course, despite of not being in thermodynamic equilibrium, we all don't ignite spontaneously, as there is an energetic barrier preventing this. In order to overcome this energetic barrier, we would have to put in some energy first, usually in the form of heat.
In the end, if we want to burn something, we want to create a chain reaction. Create enough energy (heat) to overcome the energy barrier for the oxidation of organic matter with oxygen from the air. Then, if more matter oxidizes, more heat is created, facilitating the oxidation of even more matter, and so on. Water on the other hand serves as a very efficient heat sink, as it is one of the most (energetically) expensive materials to warm up. And evaporating water needs a lot of energy, it really likes it liquid state because of the hydrogen bonds between its molecules.
So if you hold your lighter on a piece of wet wood, most of the energy will be taken up by heating or evaporating water, and almost nothing will go into facilitating the oxidation of the wood.