SELECT
a.foo
b.bar
c.foobar
FROM tableOne AS a
INNER JOIN tableTwo AS b ON a.pk = b.fk
LEFT JOIN tableThree AS c ON b.pk = c.fk
WHERE a.foo = \'something\'
AND c.foo         
        
The reason you're seeing this is because the left join sets all columns of c to NULL for those rows that don't exist in c (i.e. that can't be joined). This implies that the comparison c.foobar = 'somethingelse' is not true, which is why those rows are not being returned.
In the case where you move the c.foobar = 'somethingelse' into the join condition, that join is still returning those rows (albeit with NULL values) when the condition is not true.