It’s the rod that keeps the door from swinging open freely. It’s between the hinges and attaches to both the door and the body of the car. When you open the door, it provides resistance and then keeps the door open at an angle unless you push it more.
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Why is it called a strap if it’s made of metal?
Because they used to be made of leather.
Venturing into speculation, I’d guess it’s because at one time they actually were fabric straps instead of being built into the hinges. In searching for an image, I found fabric check straps to be still available.
EDIT: Ninja’d by beowulf!
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It appears no one sells these things and the ones that claim to sell them are just mislabeling things. 
Get it from a junkyard.
They should be really easy to find. Any parts store should have them or be able to get them, or the dealer will have them.
Also, Jeep Wranglers are the only vehicles I can think of that still have straps, but they’re nylon instead of leather.
Because straps can be made of metal.
Automotive door check straps are not commonly (if at all) available through the aftermarket. Contact a dealer for the particular make of vehicle.
Confirmed: My 95 Jeep has one on each door.
??? Your point? Every car out there has one on each door.
I believe FuzzyOgre was pointing out that the '95 Jeep has fabric (nylon) check straps. Most cars have metal ones.
Wranglers have nylon/fabric straps that are easy to slip off to facilitate door removal.
My car has three on the front left door and two on the right front door. It also has two headlights on the left and one on the right.
Ok gotta ask, what kind of car is that? If you don’t mind a pic or link would be nice. As to the OP a junkyard or pick a part would be the place to get these IMHO
Capt
Well, it’s a '49, '50, '51, '52, '53, '54, '55, '56 '57, '58, '59 automobile. It’s a '60, '61, '62, '63, '64, '65, '66, '67 '68, '69, '70 automobile. 