adicionando informações personalizadas no gráfico via matplotlib usando python

Uma maneira de fazer isso é usar matplotlib.axes.Axes.annotate com um estilo de seta adequado e argumento annotation_clip definido como False:

import matplotlib.pyplot as plt

# plot curves
curve_A = [6, 4, 2, 8]
curve_B = [12, 3, 1, 9]
x = range(len(curve_A))

fig = plt.figure()
ax = fig.add_subplot()
ax.plot(curve_A)
ax.plot(curve_B)

# make sure the curves "touch" the axes on the left
ax.set_xlim(x[0])

# get all limits 
x_min, x_max = ax.get_xlim()
y_min, y_max = ax.get_ylim()

# define the annotation offset from the minimum x to the left
offset = 0.2

# annotate the first y-value of the curve A, placing the text below
ax.annotate("\nText A", (x_min - offset, curve_A[0]), (x_min - offset, y_min),
            xycoords='data', textcoords='data',
            size='large', color='k',
            horizontalalignment='center', verticalalignment='top',
            arrowprops=dict(
                arrowstyle='<->',
                shrinkA=0,
                shrinkB=0
            ),
            annotation_clip=False  # required to see the annotation outside of the axes
            )

# annotate the first y-value of the curve B, placing the text above
ax.annotate("Text B\n", (x_min - offset*2, y_min), (x_min - offset*2, curve_B[0]),
            xycoords='data', textcoords='data',
            size='large', color='k',
            horizontalalignment='center', verticalalignment='bottom',
            arrowprops=dict(
                arrowstyle='<->',
                shrinkA=0,
                shrinkB=0
            ),
            annotation_clip=False  # required to see the annotation outside of the axes
            )
        
plt.show()

O resultado: