In order to go to university in Germany, you need the Abitur. The Abitur is comparable to the high school diploma. Usually, you need to go to school for 13 years in order to get the Abitur and most people are 18 to 20 years old when they get their Abitur.
In the United States, you need a high school diploma, which takes 12 years of school. Most people are about 18 when they get their high school diploma.
The German Abitur puts more emphasis on academic topics like math, physics, chemistry than the American high school diploma, which leaves the student a greater variety of classes, partly more practically oriented topics like wood working or agriculture.

At an American University, you get your Bachelors Degree after four years. At some schools, you also get an Associates Degree after 2 years. After the Bachelors degree, you can go on to get the Masters degree for about another 2 years or, for some majors, go directly into a Doctorate program, which takes approximately three to seven years.
In Germany, it takes about 2 years to get the Vordiplom and then another approximately three to four years to get the Diplom at a regular university.

There are big differences in the application of the degrees of one country to the system in the other country.

In Germany, some schools see the Bachelors degree as being equal to the Vordiplom, while at the same time, in the United States, the Vordiplom is treated like an Associates degree.
If you go to the United States with a Diplom, it will most likely be counted as a bachelors degree. If you go to Germany, wanting to get a German Diplom for your American degree, you will most likely need a Master's degree.

It seems like both countries think of their educational system as more valuable than that of the other country. One of the problems may also be that the whole process and the involved class work is quite different in both countries, it is a classic example of comparing apples and pears.