Simply put, a federal constitution is a document that sets out the relationships between the governors and the governed under a federal system of government. Federal constitutions vary, but they tend to set out in considerable detail the precise nature of such relationships, as it is vitally important in a federal system to know where power lies and under what conditions it is to be exercised.
Why is this important? Well, a federal system of government involves the sharing of power between a national or federal government and state and local governments. To take an obvious example, in the United States, there is the federal government in Washington, DC as well as state governments—fifty in total—and local governments, which operate at a level below that of the states.
For such a system to operate effectively, it's essential for the precise division of powers and responsibilities to be set out clearly in the relevant federal constitution. In the case of the United States, this of course means the US Constitution.
Even so, no matter how carefully a federal constitution is drafted, it simply isn't possible to avoid conflict between different levels of government concerning the appropriate exercise of power. The US Constitution has always been as much contested as revered, and there continues to be debate on the question of which powers belong to the federal government and which to the states.
Over the years, the question of the appropriate balance of power between the federal government and the states has resulted in a fair amount of litigation, most of which has tended to lead to an increase in federal power at the expense of the states. Among other things, what all this litigation tells us is that, no matter how well-drafted a constitutional document is, it is always wide open to many different, and occasionally conflicting, interpretations.