An inner join of A and B gives the result of A intersect B while outer join of A and B gives the results of A union B.
Examples
Suppose you have two Tables, with a single column each, and data as follows:
A B
- -
1 3
2 4
3 5
4 6
Note that (1,2) are unique to A, (3,4) are common, and (5,6) are unique to B.
Inner join
An inner join using either of the equivalent queries gives the intersection of the two tables, i.e. the two rows they have in common.
select * from a INNER JOIN b on a.a = b.b;
select a.*,b.* from a,b where a.a = b.b;
a | b
--+--
3 | 3
4 | 4
Outer join
A outer join will give you the union of A and B, i.e. All the rows in A and all the rows in B. If something in A doesn't have a corresponding datum in B, then the B portion is null, and vice versa.
select * from a FULL OUTER JOIN b on a.a = b.b;
a | b
-----+-----
1 | null
2 | null
3 | 3
4 | 4
null | 6
null | 5