The $3$ Euler angles (usually denoted by $\alpha, \beta$ and $\gamma$) are often used to represent the current orientation of an aircraft.
Starting from the "parked on the ground with nose pointed North" orientation of the aircraft, we can apply rotations in the Z-X'-Z'' order:
- Yaw around the aircraft's Z axis by $ \alpha $
- Roll around the aircraft's new X' axis by $ \beta $
- Yaw (again) around the aircraft's new Z'' axis by $ \gamma $
to get the current orientation of the aircraft represented by the $3$ Euler angles $(\alpha, \beta, \gamma)$.
You may have noticed that we yaw twice, and we never use pitch. In fact, there are many ways of describing the orientation of an aircraft (or other rigid objection), some of which use all three: some amount $a$ of yaw, then some amount $b$ of pitch, then some amount $c$ of roll.
There exist standard formulas for converting between different ways of describing some given orientation: orientation in $(a, b, c)$ format; orientation in Euler angle $ ( \alpha, \beta, \gamma ) $ format; orientation as described by a $3 \times 3$ rotation matrix, etc.
I'm assuming one popular coordinate system in flight dynamics which associates:
- X-axis is positive forward, through the nose of the aircraft
- Y-axis is positive out the right wing
- Z-axis is positive down.