Let nu be a nondecreasing concave sequence of positive real numbers and 1 <= p < infinity. In this note, we introduce the notion of modulus of p-variation for a function of a real variable, and show that it serves in at least two important problems, namely, the uniform convergence of Fourier series and computation of certain K-functionals. Using this new tool, we first define a Banach space, denoted V-p[nu], that is a natural unification of the Wiener class BVp and the Chanturiya class V[nu]. Then we prove that V-p[nu] satisfies a Helly-type selection principle which enables us to characterize continuous functions in V-p[nu] in terms of their Fejer means. We also prove that a certain K-functional for the couple (C, B V-p) can be expressed in terms of the modulus of p-variation, where C denotes the space of continuous functions. Next, we obtain equivalent optimal conditions for the uniform convergence of the Fourier series of all functions in each of the classes C boolean AND V-p[nu] and H-omega boolean AND V-p[nu], where omega is a modulus of continuity and H-omega denotes its associated Lipschitz class. Finally, we establish sharp embeddings into V-p[nu] of various spaces of functions of generalized bounded variation. As a by-product of these latter results, we infer embedding results for certain symmetric sequence spaces.