what is a drive-shaft and why we need it in a car?
I do get the point of having crankshaft (using Wikipedia) but still confuse with drive-shaft
It's used on front engine rear wheel drive and most 4 wheel drive vehicles it couples the transmission with the rear differential.
In the picture above you can see the driveshaft where it's connected to the pinion on the rear end. The drive shaft is the part on the lower right side of the picture. The other end of it would be connected to the transmission.
On front wheel drive cars the driveshaft is not used. The transmission and differential is combined into one unit called a transaxle.
Another view below shows a both the transmission and the rear differential.
Here is an exploded view of a drive shaft
Here is a car with a rear transmission and the engine up front. They do this for weight balance. The driveshaft is inside the torque tube. That's the tube you see in the middle of the picture.
Driveshaft transfers power from a remotely mounted engine (in the old days, one would say transmission here, but at least one modern car has the transmission all the way back on the drive wheels) to drive wheels. Example, a front engine car with rear wheel drive will have a driveshaft connecting them.