What does "taken up" mean in this paragraph?
The purpose of adjusting entries is to update the accounts to conform with the accrual concept. At the end of the accounting period, some income and expenses may have not been recorded, taken up or updated; hence, there is a need to update the accounts.

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Taken up, in this context, means it was never used. If I had a been given an allowance of $100 to spend on food and I only spent 45 then  55 had not been taken up and is therefore still available

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In this scenario it was never recieved. It could not be recorded because they never got the information. Since it was never recorded, it could not be updated.