Allowance, Spending Money
noun
If 遣う is something along the lines of "to consider" then a "small consider" is what I'll give you for your spending money. Can I have some money? $50? No, how about a smaller consideration on that, maybe something that's more along the lines of an allowance?
こづかい
The reading is the alternate reading of 小 and 遣う's reading. Watch out for the rendaku.
お子さんには月々お小遣いはいくら渡しているんですか。
How much spending money do you give your kid a month?