selecting multiple categories from database
Try OR in place of AND (in where condition). try this:
$query = ("SELECT blogs_id, title, body, posted_by, category FROM blogs INNER JOIN categories ON categories.category_id=blogs.category_id where category='cat1' OR category='cat2' OR category='cat3' ORDER BY blogs_id desc LIMIT 10");
Try this
$query = ("SELECT blogs_id, title, body, posted_by, category FROM blogs INNER JOIN categories ON categories.category_id=blogs.category_id where category IN ('cat1', 'cat2', 'cat3') ORDER BY blogs_id desc LIMIT 10");