Suppose I have the following table T:
a b
--------
1 abc
1 def
1 ghi
2 jkl
2 mno
2 pqr
And I do the following query:
SELECT a, b
FROM T
GROUP BY a
The output should have two rows, one row where a=1 and a second row where a=2.
But what should the value of b show on each of these two rows? There are three possibilities in each case, and nothing in the query makes it clear which value to choose for b in each group. It's ambiguous.
This demonstrates the single-value rule, which prohibits the undefined results you get when you run a GROUP BY query, and you include any columns in the select-list that are neither part of the grouping criteria, nor appear in aggregate functions (SUM, MIN, MAX, etc.).
Fixing it might look like this:
SELECT a, MAX(b) AS x
FROM T
GROUP BY a
Now it's clear that you want the following result:
a x
--------
1 ghi
2 pqr