We make a SO for several reasons. We have a suit that we want led; we have too many values to pass, e.g. a good 10-14 hcp; we want to find out which of our suits to lead; we want to preempt at a low level; we have a hand that seems conducive to competition. So what are we overcalling on? Many times one level overcalls only have four card suits, and tend to show length in opener's suit. It denies holding a side five card suit or probably even a four card suit unless you're 4-4, 5-4 or 6-4, and no other available systemic bid describes your hand. As these overcalls are so aggressive, we cautiously raise partner. We thus employ support doubles and redoubles after an overcall and interference. Occasionally, we must conceal three card support on hands people might commonly raise with in standard. Be more conservative especially when holding three small, Jxx or Qxx of LHO's suit which is known as the "Death Holding " or a 4333 hand with a bad six or seven count.
What about suit quality? There exists no specific requirements here except that you hold four cards in that suit. For example, if holding S KQx H T9xx D xx C AKxx, and RHO opens 1 club, we would not pass but rather overcall 1 heart. The average suit quality with which someone would overcall on approximates to KJ9x. Again, these bids are all relative to vulnerability or the ability to get to another spot if necessary.
The inferences from partner passing in an auction like this: 1C - P - 1S, are very revealing. It's known that partner could not even compete at the one level. Partner almost surely denies possession of all the hands mentioned in the second paragraph on the SO, and denies also the three-suited takeouts, two-suited hands, etc., as will be described ahead. The hands most likely to be passed are 4x3 hands with length in opener's suit or any hand with opener's suit, very weak hands, and hands with a bad suit and only average values, i.e. Jxxx or worse and 6-9 HCP, depending on the hand.