How to put text outside python plots?

Looks like the text is there but it lies outside of the figure boundary. Use subplots_adjust() to make room for the text:

import matplotlib.pyplot as plt

textstr = 'NSE=%.2f\nRMSE=%.2f\n'%(1, 2)
plt.xlim(2002, 2008)
plt.ylim(0, 4500)
# print textstr
plt.text(2000, 2000, textstr, fontsize=14)
plt.grid(True)
plt.subplots_adjust(left=0.25)
plt.show()

It's probably best to define the position in figure coordinates instead of data coordinates as you'd probably not want the text to change its position when changing the data.

Using figure coordinates can be done either by specifying the figure transform (fig.transFigure)

plt.text(0.02, 0.5, textstr, fontsize=14, transform=plt.gcf().transFigure)

or by using the text method of the figure instead of that of the axes.

plt.gcf().text(0.02, 0.5, textstr, fontsize=14)

In both cases the coordinates to place the text are in figure coordinates, where (0,0) is the bottom left and (1,1) is the top right of the figure.

At the end you still may want to provide some extra space for the text to fit next to the axes, using plt.subplots_adjust(left=0.3) or so.

According to Matplotlib version 3.3.4 documentation, you can use the figtext method:

matplotlib.pyplot.figtext(x, y, s, fontdict=None, **kwargs)

or in your case

plt.figtext(0.02, 0.5, textstr, fontsize=14)

It seems to give the same result as one of the answer by @ImportanceOfBeingErnest, i.e. :

plt.gcf().text(0.02, 0.5, textstr, fontsize=14) 

I have used both commands with Matplobib version 3.3.1.