Manipulate[{ListPlot[Table[{k,PDF[BinomialDistribution[n,p],k]},{k,0,n}],Filling->Axis, AxesLabel->{Binomial, }],Plot[PDF[NormalDistribution[n p,Sqrt[n p (1-p)]],x],{x,0,n}, AxesLabel -> {Normal, }]},{n,5,60,5},{p,0.25,0.75,0.05}]

On the left, we have the Binomial Distribution, with n trials and probability p of success. On the right, we have the Normal Distribution, with mean np and variance np(1-p). You may change the paramenters n and p and observe the changes to these graphs.  The main point is that when n is large, the two distributions are close. In particular, the Binomial Distribution can be approximated by the Normal Distribution when n is large.