Creating labels where line appears in matplotlib figure

You can use something like

plt.axvline(10)
plt.text(10.1,0,'blah',rotation=90)

you might have to play around with the x and y value in text to get it to align properly. You can find the more complete documentation here.

A solution without manual placement is to use "blended transformations".

Transformations transform coordinates from one coordinate system to another. By specifying a transformation through the transform parameter of text, you can give the x and y coordinates of the text in the axis coordinate system (going from 0 to 1 from left to right/top to bottom of the x/y axes, respectively). With blended transformations, you can used a mixed coordinate system.

This is exactly what you need: you have the x coordinate given by the data and you want to place the text on the y axes somewhere relative to the axis, say in the center. The code to do this looks like this:

import matplotlib.transforms as transforms
import matplotlib.pyplot as plt

fig, ax = plt.subplots()

# the x coords of this transformation are data, and the
# y coord are axes
trans = ax.get_xaxis_transform()

x = 10
ax.axvline(x)
plt.text(x, .5, 'hello', transform=trans)

plt.show()