"A crystal is formed by a large number of repetitions of basic pattern of particles in space.
The basic structural unit which when repeated in three spatial directions generates the crystal structure is called unit cell."
Assume I take some same perfect geometrical cubes and arrange them in all three dimensional directions, a larger box similar to the smaller ones will be introduced.
From this assumption and the information above it, I deduce that a unit cell should be similar to the relevant crystal. That means, the only difference would be lying between their size.
If this is the case, why consider the geometry of unit cell and not directly the respective crystal? We know in the assumption above; the fundamental cubical boxes would be determined by same geometrical information as would the derived cubical box.
That is; if the lengths of three axes of cube are represented by letters $a,b$ and $c$ and the angles between axes are represented by Greek letters $\alpha$, $\beta$ and $\gamma$ then for a cube,
This information is general. It is for all size of cubes. Then, why to define a unit cell and think it simpler to handle with than the crystal?