there's a (thing) (doing something)

"There's a typhoon headed toward us" means, simply, "A typhoon is headed toward us." But the first sentence is better for telling someone about the situation of preparing for a storm. In English, we often describe a situation using "There's a ____." For example, if you hear someone's phone ringing, you say:

There's someone calling you.

If a delivery person brought a package for someone at your office, you can say:

Hey, there's a package for you.

a hurricane

A hurricane is a storm that starts in the ocean in warm areas and has high winds. It's called a "hurricane" on the east coast of the U.S. and a "typhoon" when it's in the Pacific Ocean.

(something) is headed toward (somewhere)

Something that "is headed toward" a place is moving in that direction. People usually use "headed toward ___" to talk about things in the air, like storms and airplanes, or about people who are walking:

Oh, I see Ben over there. He's headed toward us.

You wouldn't usually use "headed toward" to talk about someone moving in a car or train. The word "toward" fits best when something is able to move in any direction, unlike a car or train that has to run on a road or track. For cars and trains, you say that they are "headed to" somewhere:

Excuse me, where's this bus headed to?

People also use "headed toward" to talk about trends. You imagine what the result of a trend will be, and then say that the society, the country, or some group "is headed toward" that result:

I think the U.S. is finally headed toward an economic recovery.

They're headed toward bankruptcy if the C.E.O. can't find a way to make them profitable soon.