This case is connected to the Constitution because it held that the Commerce Clause of the Constitution can be used by Congress to justify banning racial discrimination in public accommodations.
In 1881, a set of cases called the Civil Rights Cases were decided by the Supreme Court. These cases held that the 14th Amendment could not be applied to privately owned businesses. In other words, the 14th Amendment applied only to government actions, not to the actions of private businesses. In 1964, however, the US Congress passed the Civil Rights Act of 1964. That law said that even private businesses could not discriminate on the basis of race. The Heart of Atlanta Motel sued because it wanted to continue to exclude blacks from its rooms.
In this case, the Supreme Court ruled against the motel. It ruled that the Commerce Clause gives Congress the power to regulate all businesses that are involved in interstate commerce. The Court ruled that the motel was involved in such commerce even though it was, of course, in the state of Georgia.
Thus, this case is connected to the Constitution because it says that the Commerce Clause can be used to prohibit racial discrimination by private businesses.