A hypersphere is a generalization of a sphere to higher dimensions. While a regular sphere exists in three-dimensional space, a hypersphere can exist in four or more dimensions. The most common example is the 3-sphere, which is the set of points equidistant from a central point in four-dimensional space. Mathematically, a hypersphere can be defined using the equation x_1^2 + x_2^2 + ... + x_n^2 = r^2, where r is the radius and n is the number of dimensions. This concept is important in various fields, including mathematics, physics, and computer science, as it helps in understanding complex shapes and spaces.