NW=1000;nlast=100;
(*initialisation*)
For[i=1,i≤NW,i++,
x[i]=0;
];(*end for*)
dist[0]=Table[x[i],{i,1,NW}];
bc[0]=BinCounts[dist[0]/NW,{-20,20,0.1}];

(*begin time-stepping*)
For[n=1,n≤nlast,n++,
(*begin random-shifting the walkers*)
For[i=1,i≤NW,i++,
shift=2RandomInteger[]-1;
x[i]=x[i]+shift;
];(*end for*)
dist[n]=Table[x[i],{i,1,NW}]/NW;
bc[n]=BinCounts[dist[n],{-20,20,0.1}];
];(*end for*)

Manipulate[
BarChart[bc[n],PlotRange->{0,1}],{n,0,nlast,1}]

BarChart[bc[2]]