The purpose? Laziness mostly. When people are speaking informally it is reasonably common to omit the 'do' simply because it is quicker and a more 'relaxed' way of speaking. Everyone knows the 'do' is implied.

"Do you want my help?" Is a question "You want my help?" Is more of a statement. So someone could said "Do you want my help to finish your homework?" When they see someone is struggling. Or you could be in the same situation but the person struggling with their homework could say "I can't do this, how did you finish your work?" And the person could reply "You want my help?" As in the person knows the person struggling wants their help and is just asking as a formality. However you can usually use both. It's not something I would worry too much about and it's not something you can make a mistake in by not using do or using it.

The correct way to ask the question is to use the word “Do” at the start of the question. When someone omits the “do,” it is simply understood that they’re asking “Do you want my help?” It is not really correct to omit the “do” but people often will omit it. I hope that helps you a bit.

You would never drop "do" if you don't know the other person well, or if it's a business or formal context. Using the standard question format (do you want...?) is always your first option, unless you definitely know the other person accepts the "lazy" form. (Paul's right - it is lazy!!)