matplotlib: how to draw a rectangle on image

You need use patches.

import matplotlib.pyplot as plt
import matplotlib.patches as patches

fig2 = plt.figure()
ax2 = fig2.add_subplot(111, aspect='equal')

ax2.add_patch(
     patches.Rectangle(
        (0.1, 0.1),
        0.5,
        0.5,
        fill=False      # remove background
     ) ) 
fig2.savefig('rect2.png', dpi=90, bbox_inches='tight')

From my understanding matplotlib is a plotting library.

If you want to change the image data (e.g. draw a rectangle on an image), you could use PIL’s ImageDraw, OpenCV, or something similar.

Here is PIL’s ImageDraw method to draw a rectangle.

Here is one of OpenCV’s methods for drawing a rectangle.

Your question asked about Matplotlib, but probably should have just asked about drawing a rectangle on an image.

Here is another question which addresses what I think you wanted to know:
Draw a rectangle and a text in it using PIL

There is no need for subplots, and pyplot can display PIL images, so this can be simplified further:

import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
from PIL import Image

im = Image.open('stinkbug.png')

# Display the image
plt.imshow(im)

# Get the current reference
ax = plt.gca()

# Create a Rectangle patch
rect = Rectangle((50,100),40,30,linewidth=1,edgecolor='r',facecolor='none')

# Add the patch to the Axes
ax.add_patch(rect)

Or, the short version:

import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle
from PIL import Image

# Display the image
plt.imshow(Image.open('stinkbug.png'))

# Add the patch to the Axes
plt.gca().add_patch(Rectangle((50,100),40,30,linewidth=1,edgecolor='r',facecolor='none'))

If you have a set of coordinates of ordered points you can also use the plot function and plot them directly without using the Rect patch. Here I recreate the example proposed by @tmdavison using that:

import matplotlib.pyplot as plt
import matplotlib.patches as patches
from PIL import Image

im = Image.open('/content/stinkbug.png')

# Create figure and axes
fig, ax = plt.subplots()

# Display the image
ax.imshow(im)

# Coordinates of rectangle vertices
# in clockwise order
xs = [50, 90, 90, 50, 50]
ys = [100, 100, 130, 130, 100]
ax.plot(xs, ys, color="red")

plt.show()