Should not the what the majority of the people want be the law?
No. Goodness, no. One of the roles of the government is to protect the minority from the majority. If mob rule controlled everything, we'd probably still have legal slavery. Or Jim Crow laws. Or forced religious observance.
If each state can make its own laws, why do you have a central government?
For example, if central government passed a law to ban the death penalty, each state could bypass that by passing a law to allow it.
Not exactly. The tenth amendment states, "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people." Which means that the federal government's ability to write law is enumerated within the bounds of the constitution. If it's not enumerated there, then it can differ from state to state. The fourteenth amendment makes the Constitution apply to all of the states (minimum protections).
If Congress managed to pass an amendment abolishing the death penalty, and the states ratified it, there wouldn't be an ability to create a new one around it. However, if the Supreme Court declares it Unconstitutional, it's all going to depend on the wording of the decision. That's why we have such a hodgepodge of laws right now regarding gay marriage.
Or, on a day to day level, does each state have different driving laws? Like speed limits etc.
Yes. Sometimes drastically different.
How can the average person possibly know what is legal in one state and illegal a mile up the road in the next state?
Educate yourself. Ignorance of the law is not an excuse to commit a crime.
Bear in mind - the US is freaking huge. Each state has some laws that are different, sure, but I bet France and the UK have some laws that are different, too. California, if it were a country, would be the fifth largest economy in the world. Cali has a little over 38 million residents. The UK has 63 million.
Each state has it's own culture, values, economy, etc.