To be "overwhelmed" means to get so much of something that it becomes a problem. You can become "overwhelmed" with things like e-mail messages, job applications for a position that you're hiring for, parenting responsibilities, homework, etc. For example:
I'm starting to feel overwhelmed. I've got school, band practice, work, not to mention spending time with my boyfriend. I just can't handle it all!
You state the thing that is overwhelming you with the phrase "overwhelmed with ___":
It's easy to get overwhelmed with the amount of work here if you don't have an organized system for handling it all.
You may also hear "overwhelmed by ___". This is more often used to express a positive emotional feeling when something makes you so happy, thankful, or proud that you just can't believe it:
I've been overwhelmed by all the support and help my fans have given me.
I was overwhelmed by the beauty of the Italian countryside.