There should be single WHERE clause.
SELECT notes.project_id, notes.title, notes.description 
FROM notes, project_members 
WHERE 
(notes.title LIKE '%second%' OR notes.description LIKE  '%second%')
AND notes.project_id = project_members.project_id AND project_members.user_id = '7';
Query would look something above to AND between your LIKE conditions. 
You may also consider using JOIN, Like this.
SELECT notes.project_id, notes.title, notes.description 
FROM notes
JOIN project_members
ON notes.project_id=project_members.project_id
WHERE 
    (notes.title LIKE '%second%' OR notes.description LIKE  '%second%')
AND project_members.user_id = '7';