1. Yesterday morning, the car wouldn't start.
2. Yesterday morning, the car didn't start.
Is there any difference in meaning between #1 and #2?
I really don't understand about the usage of would here. Can you explain about the use of would in this case?
There is no difference in meaning. The usage of "wouldn't" gives the car almost human properties - it equates to "the car refused to start"! Of course, cars are inanimate but we frequently talk about them as if they were alive.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.