hello earthtomummy,
just to tide you over until the real experts rock up 
...i thiiiink 'higher order function' means the more sophisticated things our brains do beyond moving our muscles,reacting to pain etc
so stuff like...
How we think about time ,sequencing and abstract thoughts and concepts.
Problem solving.
How we respond to/process/integrate sensory information ...eg how we filter out unwanted stimuli? too much or not enough?
To what extent we are able to control our impulses...
What our perception is like...so stuff like you and i can 'see' a drop when there is a step...and can tell when we are walking from grass onto tarmac...without difficulty or even thinking aboutit...cos we perceived all th enecessary info about depth texture etc
There is something called 'central coherence' which sort of relates to how you perceive things. its about filtering and consolidating the information you see hear,feel etc.
e.g. Do you get the gist/jist of a conversation/situation or get caught up in a weeny detail...do you see the the whole pram or the patterns made by the rain on the hood?
I think imagination in thi s context may not be limited to creative thought and artistic leanings but maybe about stuff like anticipation,what ifs? and being able to think of different outcomes.it might include being able to plan and think ahead.
hth x