What is the 'ask me a question' feature

I've signed up for it expecting to get alerts to answer questions about my interests? Is this correct? Or is that just category/question watching? In which case, what exactly is 'ask me a question'?

yes like stephanief said they send you an email notification, but also if you get asked a question a little box will appear on your profile above your comments that says my pending questions

well the ask me a question feature allows you to ask that specific person a question, but the question is still posted publicly here and can also be answered by others. it's like saying hey, I want other people to read and answer this, but I want to make sure YOU respond to it too

The ask me a question feature posts a public question. If you are here to answer questions about your interests, browse the categories (on the left) and answer the questions.

thanks for the answers... And how am I alerted to questions I'm asked - is there an icon next to the questions? do I get an email alert?

Yes.
Just make sure you have your settings set for you to receive an e-mail notification. This is how you do that: go to your profile, on the left side bar click edit my profile and then click Manage Question Alerts.