Initial Side
The initial side of an angle in standard position is the fixed ray along the positive x-axis from which the angle is measured.
Definition
The initial side is the starting, fixed ray of an angle in standard position, always pointing to the right along the positive $x$-axis; rotation from the initial side to the terminal side, measured counterclockwise as positive, defines the angle. Formally, it corresponds to the identity element of the rotation group $SO(2)$, zero rotation from the standard orientation, and the choice of initial side is a gauge choice: changing it amounts to an overall phase shift in the angle parametrization.
Example
When you draw any angle in standard position, the initial side is the fixed arm pointing right, while the other arm (the one that moves) is the terminal side; for a $120^\circ$ angle, the terminal side is rotated $120^\circ$ counterclockwise from it. In navigation, the initial side might be North instead of East, and converting between math convention (East $= 0^\circ$, counterclockwise positive) and compass convention (North $= 0^\circ$, clockwise positive) requires compass bearing $= 90^\circ - \text{math angle}$.
Key Insight
"Initial" means beginning, the ray where rotation starts before you measure the angle, and by convention all angles in standard position share the same initial side, which is what makes coterminal angles possible. The initial side defines the branch cut for the argument function in complex analysis: the principal argument $\text{Arg}(z)$ in $(-\pi, \pi]$ uses the negative real axis as a branch cut, equivalent to choosing a different "initial side" for measuring angles.