It would be helpful if you could ask a little bit more specific of a question since there really is a great deal to be said about the 1920s and the automobile and Henry Ford.
Henry Ford is connected to the 1920s because it was his pioneering use of the assembly line in the 1910s that made the car so common in the 1920s and so important to the culture of that decade. The assembly line made it much easier, quicker, and cheaper to produce cars. This meant that the price of the cars could drop and many more people could afford them.
Affordable cars became a major contributor to the culture of the '20s. They allowed people to do many more things for fun and they allowed people to have more freedom and mobility than they had previously enjoyed. This helped lead to the more open and fun-oriented culture of the "Roaring '20s."
The main connection, then, between Ford, cars, and the '20s is that Ford's use of the assembly line made cars cheaper and more easily available. This, in turn, helped lead to major changes in the culture of the '20s.