What happens when we connect a external emf (having emf greater than that of emf of a galvanic cell) to a galvanic cell? I read a statement given in the book and I did not understand it

"If any external battery is connected whose emf is more than the emf of galvanic cell ,then it will act as Electrolytic cell"

Also can you please explain what happens if we connect a external battery having emf less than that of galvanic cell?
Think of a generic redox pair:
$$\ce{Ox + ne- -&gt; Red}$$
and use Nernst equation (and a few simplifications) to calculate its potential:
$$ E = E^\circ + \frac{\mathrm{RT}}{\mathrm{nF}}\mathrm{ln}\left(\frac{[Ox]}{[Red]}\right)$$

So, now you know what potential you would measure on such a half-cell. However, what would happen if you applied some arbitrary potential $E_{w}$ ?

Well, if $E_{w} &gt; E$, then that also means that 
$$\frac{\mathrm{RT}}{\mathrm{nF}}\mathrm{ln}\left(\frac{[Ox]_w}{[Red]_w}\right) &gt; \frac{\mathrm{RT}}{\mathrm{nF}}\mathrm{ln}\left(\frac{[Ox]}{[Red]}\right)$$

Finally, you get that this situation implies an increase of $\ce{Ox}$ at the expense of $\ce{Red}$, which is what you would expect from an electrolytic cell - the supply of electrical energy causes electrochemical reactions.

If you apply a potential that is below $E$, the only difference would be that $\ce{Ox}$ would decrease and $\ce{Red}$ would increase, but the overall treatment remains the same.