Simple example. Let’s select students with grades using left outer join:
SELECT DISTINCT s.id
FROM students s
LEFT JOIN grades g ON g.student_id = s.id
WHERE g.student_id IS NOT NULL
Now the same with left semi-join:
SELECT s.id
FROM students s
WHERE EXISTS (SELECT 1 FROM grades g
WHERE g.student_id = s.id)
The latter is generally more efficient (depending on concrete DBMS and query optimizer).