Your logic is not entirely clear. You must enclose the logical subordinate clauses in parentheses so that MySQL knows what you really want.
Do you want to
ad_status='1'
    AND (ad_region='Location One' OR ad_region='Location Two' OR ad_region='Location Three')
    AND ad_type='For Rent'
?
If you do this, you are probably better off using IN(), for example:
SELECT * FROM ads 
WHERE ad_status='1'
    AND ad_region IN ('Location One', 'Location Two', 'Location Three')
    AND ad_type='For Rent' 
ORDER BY ad_id 
DESC LIMIT 10
;
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