Plz explain me in an easy way what this theorem says and an example

utTEdSIn9, TEaSITg, TetX = Ini S and proce Ini Sand proceed in a sir TeL lar mann Lemma (On nested intervals). Let the sequence of the intervals {[a, b]} be such that [a b cla, b] Vn e N (such intervals are called nested), and their lengths converge to zero, i.e., lim n- (b- a)= 0. Then there exists a unique point that belongs to every interval, i.e., e la, b] vn e N, and 5- lim a, = sup{a,) = lim b, = inifb,}. no n0