Evaporation of water
Evaporation is a surface phenomenon, boiling is a bulk phenomenon.  Evaporation will always be occurring for any liquid with an exposed surface.  Water molecules in a liquid sample have a distribution of kinetic energies.  It takes less work for a surface water molecule to break free from its neighbors, then for a water molecule in the bulk to escape, since the former has fewer neighbors (no molecules on top).  Those molecules with enough kinetic energy to break away from their neighbors will escape.

For water to boil its vapor pressure must equal the atmospheric pressure.

The only requirement for evaporation to occur is an exposed liquid surface.  I don't think relative humidity affects the boiling point, but I suspect it would affect the rate at which a liquid will evaporate from an open container.  Evaporation is always occurring, but to notice a change in the amount of material in an open system, more material must leave the surface then returns to the surface and the rate of return will be affected by the composition (water content) of the air above the open sample.