A guy may have the best of intentions, but sometimes he may accidentally grab a boob. These things happen.
Sometimes you put an arm out to stop someone, or crash into someone, or they fall on top of you. Sometimes that someone is a girl, and sometimes, if the planets are aligned just right, you accidentally touch or grab her breasts. In some ways this is the opposite to the Skinship Grope, though this concept sometimes leads onto that one.
The concept name is a play on the phrase Thanks for the memory.
Though occasionally done for comical purposes, this is largely regarded as a fan service concept, and thus is seen most often in harem or otherwise fan service-themed series. When they aren't crashing into them face-first, male characters (or sometimes female) who crash into cute girls often land in awkward positions. After the dust settles they find something soft has found it's way into one of their hands, sometimes even both, and after a squeeze or two it becomes obvious what that soft thing is. This will usually result in one of three responses from the girl: