I don't understand the first graph...because if V1 ever becomes positive, there won't be any current in V0(diode)??
but in the graph V0 keeps getting larger as v1 increases to some positive voltage..
Can someone please explain to me what i'm missing in this graph???

 

When the voltage across the diode is +ve, the diode is off.
this means that whatever voltage is applied in the input side
is seen in the output.
so vin=vout
Remember that when the diode is off it acts like an open circuit.
in your case replace the diode with an open circuit and you will
get that same graph.