What is "The American Dream" and is it still on?

I had a very interesting discussion with an American friend about the American Dream. He explained it to me something like that every man has the opportunity and responsibility to achieve success alone. To make it short.

Is the American Dream the fundamental of the capitalist ideology in America? In my ears it sounds as if the American Dream is about financial success – earn lots of money and you are living the dream. But I also have a feeling that the Dream is unjust and unfair. Not everyone can achieve the financial success the Dream “talks” about. It all depends on things such as area of living, family history, social class, ethnicity, gender, health etc.

I have only studied American social studies for a month or so in Uni, but I remember a professor talking about this and he said something like: The American Dream doesn’t work. If it did USA wouldn’t be such a segregated country where the real workforce who built the country hasn’t received the credit it deserved.
Does he have a point?

I also feel that the American Dream is built on others burden. Back in history,it was the slave owners who became successful up on their high horses, but the slaves, the workers, got nothing. The successful today are kinda the same everywhere you go, even here in Sweden. High bank people in our biggest banks receive huge bonuses even in days like these – first they ask the state for help and then they pay out bonuses. Loan institutes make money on broke families who cannot keep their houses etc.
Is the American Dream only for those who don’t mind stepping on others, who are controlled by greed?

I might be mixing things up here and I know little about how it works, but I am very interested in US social studies and would love some feedback and lessons on the topic :) Most of all I want to come visit you!

Have a great day!