"Currently" means "now" but sounds a lot more formal and professional. It's used in a lot of business situations. For example, you can use it on your voice mail message at work:
Hi, you've reached Aaron. I'm currently unavailable, but please leave a message and I'll get back to you as soon as I can.
In the example at top, the speaker says that he is "currently employed as..." That means that he has a job right now. In the U.S., it's common to apply for a new job and go on interviews while you're still at your previous job.