diff --git a/lib/matplotlib/colors.py b/lib/matplotlib/colors.py
index 71647cbef94d..a26a7a01557c 100644
--- a/lib/matplotlib/colors.py
+++ b/lib/matplotlib/colors.py
@@ -1247,25 +1247,29 @@ class BoundaryNorm(Normalize):
     """
     def __init__(self, boundaries, ncolors, clip=False):
         """
-        *boundaries*
-            a monotonically increasing sequence
-        *ncolors*
-            number of colors in the colormap to be used
-
-        If::
-
-            b[i] <= v < b[i+1]
+        Parameters
+        ----------
+        boundaries : array-like
+            Monotonically increasing sequence of boundaries
+        ncolors : int
+            Number of colors in the colormap to be used
+        clip : bool, optional
+            If clip is ``True``, out of range values are mapped to 0 if they
+            are below ``boundaries[0]`` or mapped to ncolors - 1 if they are
+            above ``boundaries[-1]``.
+
+            If clip is ``False``, out of range values are mapped to -1 if
+            they are below ``boundaries[0]`` or mapped to ncolors if they are
+            above ``boundaries[-1]``. These are then converted to valid indices
+            by :meth:`Colormap.__call__`.
 
-        then v is mapped to color j;
-        as i varies from 0 to len(boundaries)-2,
-        j goes from 0 to ncolors-1.
+        Notes
+        -----
+        *boundaries* defines the edges of bins, and data falling within a bin
+        is mapped to the color with the same index.
 
-        Out-of-range values are mapped
-        to -1 if low and ncolors if high; these are converted
-        to valid indices by
-        :meth:`Colormap.__call__` .
-        If clip == True, out-of-range values
-        are mapped to 0 if low and ncolors-1 if high.
+        If the number of bins doesn't equal *ncolors*, the color is chosen
+        by linear interpolation of the bin number onto color numbers.
         """
         self.clip = clip
         self.vmin = boundaries[0]
@@ -1304,6 +1308,13 @@ def __call__(self, value, clip=None):
         return ret
 
     def inverse(self, value):
+        """
+        Raises
+        ------
+        ValueError
+            BoundaryNorm is not invertible, so calling this method will always
+            raise an error
+        """
         return ValueError("BoundaryNorm is not invertible")