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C. Watari [12] obtained a simple characterization of Lipschitz classes $Li{p}^{\left(p\right)}\alpha \left(W\right)(1\ge p\ge \infty ,\alpha >0)$ on the dyadic group using the $L^p$-modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces $B_{p,q}^{\alpha }$ on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces $B_{p,q}^{\alpha }$ by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality of the...