Allowance
Spending Money
noun
遣う means "to use," so a "small use" refers to what you can do with your spending money. You're not rolling in dough over here, so you can only use your spending money on small things. Think of it like a little allowance you can use to buy baseball cards and bubblegum and stuff.
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?