To 'scootch' is to move a little bit. Most often heard in the phrase "scootch over", but you can also 'scootch up' (move forward a bit), 'scootch back', or 'scootch together'. One usually scootches when sitting, and when you scootch you will probably be moving either your bottom or your chair. One would not scootch standing up. One might scootch while lying down.
Scootch is still new enough to qualify as slang, as least in so far that it appears in no standard dictionaries. It is a word used mostly with children (and to a lesser extent in my experience, by children), and informally amongst adults.
It is almost certainly derived from 'scoot', as used in the phrasal verb 'scoot over' (meaning 'to move over a little bit'). But 'scoot over' traditionally holds implications of a fast, swift motion, as scoot usually means 'to move at high speed'. There is no obvious bridge to the modern usage of 'scoot/scootch over' to refer to smaller, slower movements. Both of these may have been influenced by the word 'scrooch', meaning to crouch, squeeze, or huddle, as one often has to scootch/scoot over so that someone else can squeeze in beside you. Scootch may also be related to the Yiddish/German 'Rutsch mal' often said simply 'Rutsch', meaning, basically, scootch over.
I am very curious to know if this is a word found only in America, or if it is also used in the UK, Canada, Australia, etc. Please /msg me if you have any information to add.
The UK noders speak:
The Debutante says re Scootch: Hmm. I don't use 'scootch' and I'm not sure if I've heard anyone else use it here. If I want to ask people to shuffle over I seem to use 'hutch up', but I'm not sure how common that is, either.
Wntrmute says re Scootch: I've heard it used here in the UK, in the same context as you suggest of moving when sitting, such as adjusting a car seat for the benefit of other passengers.
call says re Scootch: I always thought that 'scootch' was Scottish in origin. It's been in use here as long as I can remember.
spiregrain says re Scootch: 'round these parts, we say "budge up" or "budge over" in contexts where, (I understand from US sit-coms) you lot say "scootch". However, due to said sit-coms, we are familiar with "Scootch", but tend not to use it as much as "budge". Yet.
And the Aussies:
kalen says re Scootch: A high level of familiarity with the word -- and occasional use -- in Australia, probably from US sit-coms. "Shove over" or simply a meaningful look are the usual devices for achieving the same purpose.
More on possible orgins:
maxClimb says re Scootch: "scoot yourself over" said quickly leads to "scootch 'self over" which leads to 'scootch over', etc.