The Day Master is the Heavenly Stem of your Day Pillar in a Ba Zi chart — the elemental representation of your core self. Every other element in your chart is interpreted in relation to it.
Short answer
The Day Master is the Heavenly Stem of your Day Pillar in a Ba Zi chart — the elemental representation of your core self. Every other element in your chart is interpreted in relation to it.
In depth
There are 10 possible Day Masters: Yang Wood (甲), Yin Wood (乙), Yang Fire (丙), Yin Fire (丁), Yang Earth (戊), Yin Earth (己), Yang Metal (庚), Yin Metal (辛), Yang Water (壬), and Yin Water (癸).
Your Day Master determines whether other elements in your chart act as Resource, Output, Wealth, Authority, or Friend (the "Ten Gods" framework). For example, if your Day Master is Yang Wood, then Water is your Resource (it nourishes you), Fire is your Output (you produce it), Earth is your Wealth (you control it), Metal is your Authority (it controls you), and Wood is your Friend.
Reading a Ba Zi chart without first identifying the Day Master is impossible — it is the reference point for every other interpretation. Two charts with identical stems and branches will read entirely differently if the Day Master is in different elemental positions.