Backport PR #51788 on branch 2.0.x (DOC: Add section about copy on write and mutating objects) (#52006)

Backport PR #51788: DOC: Add section about copy on write and mutating objects

Co-authored-by: Patrick Hoefler <61934744+phofl@users.noreply.github.com>

Author: meeseeksmachine

doc/source/user_guide/copy_on_write.rst

@@ -6,11 +6,6 @@
 Copy-on-Write (CoW)
 *******************
 
-.. ipython:: python
-    :suppress:
-
-    pd.options.mode.copy_on_write = True
-
 Copy-on-Write was first introduced in version 1.5.0. Starting from version 2.0 most of the
 optimizations that become possible through CoW are implemented and supported. A complete list
 can be found at :ref:`Copy-on-Write optimizations <copy_on_write.optimizations>`.
@@ -21,6 +16,36 @@ CoW will lead to more predictable behavior since it is not possible to update mo
 one object with one statement, e.g. indexing operations or methods won't have side-effects. Additionally, through
 delaying copies as long as possible, the average performance and memory usage will improve.
 
+Previous behavior
+-----------------
+
+pandas indexing behavior is tricky to understand. Some operations return views while
+other return copies. Depending on the result of the operation, mutation one object
+might accidentally mutate another:
+
+.. ipython:: python
+
+    df = pd.DataFrame({"foo": [1, 2, 3], "bar": [4, 5, 6]})
+    subset = df["foo"]
+    subset.iloc[0] = 100
+    df
+
+Mutating ``subset``, e.g. updating its values, also updates ``df``. The exact behavior is
+hard to predict. Copy-on-Write solves accidentally modifying more than one object,
+it explicitly disallows this. With CoW enabled, ``df`` is unchanged:
+
+.. ipython:: python
+
+    pd.options.mode.copy_on_write = True
+
+    df = pd.DataFrame({"foo": [1, 2, 3], "bar": [4, 5, 6]})
+    subset = df["foo"]
+    subset.iloc[0] = 100
+    df
+
+The following sections will explain what this means and how it impacts existing
+applications.
+
 Description
 -----------