There are two ways to play the Unassuming Cue Bid.
Simple overcalls are wide ranging (8 -15) and non-forcing.
Your partner's overcalls are usually rubbish, aren't they?
LHO opens 1D and partner overcalls 1H.
You have a decent 10/11 pts. and a three or four card heart suit, but how strong is partner's overcall?
You may bid 3H and find partner with her usual pile of junk. - 1 off.
Or, you may bid 2H or even pass and miss game because on this particular ocassion partner had good values for her overcall.
The solution is, after RHO passes, to bid the opponent's suit, (2D) an Unassuming Cue Bid.
2D is asking east "how good was your overcall?" It shows an interest in bidding to a game contract without bidding too high.
This unassuming cue bid of the enemy suit usually shows support for partner's suit and a good raise. This means that you can bids 2H or 3H as pre-emptive bids.
Partner can now either bid game or show an outside feature to indicate a good quality overcall, or sign off in 2H with the usual garbage that you're used to!
If partner has opened the bidding and RHO overcalls, the Unassuming Cue Bid shows four card support for your partner and a good raise to the next level of your partner's suit.
For example - if partner opens 1H, and the opposition overcall 1S, a bid of 2S, would now show four card support for hearts and enough points for a raise to 3H (the next level of hearts).
This leaves the bid of 3H after the 1S, overcall for pre-emptive purposes used on a weaker hand with better distribution.
Partner will then repeat their suit with a minimum bid, or bid something else with a stronger hand.