I googled a bit on it and found different explanations. Some says it just depends on the region and dialect. But my text book explains that as a rule of thumb 几岁了 should be used for kids before 10 years old, and for other cases 多大了 is Ok. Could you please provide some more explanation on it?
Your textbook is right. But usage might vary. 几 generally means few, the convention that its maximum is 10, that's why you can not ask someone looking older than 10 你几岁？
Of course you could ask a little boy or girl 你多大？, that's not wrong, but do not ask an adult 你几岁/您几岁？, this wouldn't be appropriate.
The only context when 几岁 could apply to adults is 50几岁 (fifty something of age) and, of course, 30几岁,40几岁 and so on. Here 几 only refers to the 'something', the unknown few years someone is older than 50, etc.
几, when used in declarative sentence, means several, as @DrunkenMaster pointed out, using it on quantities larger than 10 feels odd.
However, this rule, when used in questions, is very relaxed. So you will see the following questions all the time
- 人有几颗牙齿? How many teeth do humans have
- 美国有几个州? How many states are there in the US
And of course, 你几岁了 can be and is used all age. Asking 你几岁了 and getting 13 back is perfectly normal and accepted. Also asking 你多大了 and getting 5 back is also normal.
The important difference is 你几岁了 is less formal than 你多大了. So adults of same age/status can easily ask 你几岁了 to each other, even in their 80s, but you'll see it less used when asking people with higher status.
I wouldn't agree with what your textbook claims to be the rule of thumb – although the rule technically applies, the common practice, as suggested in other answers, is that 几岁了 and 多大了 are applicable to all ages.
A few things to keep in mind when asking for age:
Beware that many adults are concerned with age. If you ask what's the minimum age that defines such "adults", I would say it varies. My take is that 25-year-old and above are generally concerned with age.
If you have to ask, do it with manners, especially in a formal setting. For elders (say 65 and above), a good question would be "请问您今年高寿？". For older people (say 40 to 64), a good question would be "请问您今年贵庚？". Otherwise, simply ask "您几岁了？" or "您多大了？".
Forget about the above rules IF you know the person you're asking is not conservative or traditional or is not nearly strict about courtesy.