Uniform convergence is a type of convergence for sequences of functions. A sequence of functions f_n converges uniformly to a function f on a set D if, for every small positive number ε, there exists a natural number N such that for all n ≥ N and for all x in D, the difference |f_n(x) - f(x)| is less than ε. This means that the functions in the sequence get uniformly close to the limit function across the entire set. This concept is important in analysis because it ensures that certain properties, like continuity and integration, are preserved in the limit. If a sequence of continuous functions converges uniformly to a function, then that limit function is also continuous. Uniform convergence is stronger than pointwise convergence, where the convergence may vary at different points in the domain.