A regular polygon is defined as a geometric figure where all sides are of equal length and all interior angles are of equal measure. In contrast, an irregular polygon does not possess this uniformity; its sides and angles can vary in length and measure.

To elaborate, consider regular polygons such as equilateral triangles and squares. An equilateral triangle has three sides of equal length, with each interior angle measuring $60^\circ$. A square, on the other hand, consists of four sides of equal length, and each angle measures $90^\circ$. One of the key characteristics of regular polygons is their high level of symmetry, allowing them to appear identical from multiple viewpoints, including rotations and reflections.

In contrast, irregular polygons are characterized by their lack of uniformity. This means that the lengths of their sides may differ, and their interior angles can vary as well. A prime example of an irregular polygon is a scalene triangle, where all three sides and angles are distinct. Another example is a rectangle (which is not a square), where opposite sides are equal in length, but adjacent sides differ, making it irregular with respect to side lengths, despite having angles that are all $90^\circ$.

Recognizing the difference between regular and irregular polygons is crucial for classifying shapes based on their geometric properties. This classification holds significance in various mathematical contexts, including the computation of perimeters and areas, as well as in understanding symmetry. Regular polygons typically have simpler formulas for such calculations due to their uniform properties, whereas irregular polygons may necessitate more intricate methods for analysis.