DOC: Fix DataFrame.nunique docstring and doctests (#23891)

* Remove repetition in long description

* swap sentences

Author: Moisan

ci/code_checks.sh

@@ -147,7 +147,7 @@ if [[ -z "$CHECK" || "$CHECK" == "doctests" ]]; then
 
     MSG='Doctests frame.py' ; echo $MSG
     pytest -q --doctest-modules pandas/core/frame.py \
-        -k"-axes -combine -itertuples -join -nunique -pivot_table -quantile -query -reindex -reindex_axis -replace -round -set_index -stack"
+        -k"-axes -combine -itertuples -join -pivot_table -quantile -query -reindex -reindex_axis -replace -round -set_index -stack"
     RET=$(($RET + $?)) ; echo $MSG "DONE"
 
     MSG='Doctests series.py' ; echo $MSG

pandas/core/frame.py

@@ -7279,32 +7279,43 @@ def f(x):
 
     def nunique(self, axis=0, dropna=True):
         """
-        Return Series with number of distinct observations over requested
-        axis.
+        Count distinct observations over requested axis.
+
+        Return Series with number of distinct observations. Can ignore NaN
+        values.
 
         .. versionadded:: 0.20.0
 
         Parameters
         ----------
         axis : {0 or 'index', 1 or 'columns'}, default 0
-        dropna : boolean, default True
+            The axis to use. 0 or 'index' for row-wise, 1 or 'columns' for
+            column-wise.
+        dropna : bool, default True
             Don't include NaN in the counts.
 
         Returns
         -------
         nunique : Series
 
+        See Also
+        --------
+        Series.nunique: Method nunique for Series.
+        DataFrame.count: Count non-NA cells for each column or row.
+
         Examples
         --------
         >>> df = pd.DataFrame({'A': [1, 2, 3], 'B': [1, 1, 1]})
         >>> df.nunique()
         A    3
         B    1
+        dtype: int64
 
         >>> df.nunique(axis=1)
         0    1
         1    2
         2    2
+        dtype: int64
         """
         return self.apply(Series.nunique, axis=axis, dropna=dropna)