We don't need to plt.ioff() or plt.show() (if we use %matplotlib inline). You can test above code without plt.ioff(). plt.close() has the essential role. Try this one:
%matplotlib inline
import pylab as plt
# It doesn't matter you add line below. You can even replace it by 'plt.ion()', but you will see no changes.
## plt.ioff()
# Create a new figure, plot into it, then close it so it never gets displayed
fig = plt.figure()
plt.plot([1,2,3])
plt.savefig('test0.png')
plt.close(fig)
# Create a new figure, plot into it, then don't close it so it does get displayed
fig2 = plt.figure()
plt.plot([1,3,2])
plt.savefig('test1.png')
If you run this code in iPython, it will display a second plot, and if you add plt.close(fig2) to the end of it, you will see nothing.
In conclusion, if you close figure by plt.close(fig), it won't be displayed.