diff --git a/sklearn/cluster/_mean_shift.py b/sklearn/cluster/_mean_shift.py
index b8bf585b0067d..f886fe392f4bf 100644
--- a/sklearn/cluster/_mean_shift.py
+++ b/sklearn/cluster/_mean_shift.py
@@ -176,8 +176,15 @@ def mean_shift(
         operation terminates (for that seed point), if has not converged yet.
 
     n_jobs : int, default=None
-        The number of jobs to use for the computation. This works by computing
-        each of the n_init runs in parallel.
+        The number of jobs to use for the computation. The following tasks benefit
+        from the parallelization:
+
+        - The search of nearest neighbors for bandwidth estimation and label
+          assignments. See the details in the docstring of the
+          ``NearestNeighbors`` class.
+        - Hill-climbing optimization for all seeds.
+
+        See :term:`Glossary <n_jobs>` for more details.
 
         ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
         ``-1`` means using all processors. See :term:`Glossary <n_jobs>`
@@ -312,8 +319,15 @@ class MeanShift(ClusterMixin, BaseEstimator):
         If false, then orphans are given cluster label -1.
 
     n_jobs : int, default=None
-        The number of jobs to use for the computation. This works by computing
-        each of the n_init runs in parallel.
+        The number of jobs to use for the computation. The following tasks benefit
+        from the parallelization:
+
+        - The search of nearest neighbors for bandwidth estimation and label
+          assignments. See the details in the docstring of the
+          ``NearestNeighbors`` class.
+        - Hill-climbing optimization for all seeds.
+
+        See :term:`Glossary <n_jobs>` for more details.
 
         ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
         ``-1`` means using all processors. See :term:`Glossary <n_jobs>`