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.

A federal constitution is a document that is drafted and ratified for the purpose of stating as precisely as possible the relationship of the federal government to the governed -- in effect, the people -- and the relationship of the federal government to the individual political entities (the States) that collectively comprise the nation.  One of the more intractable issues with which the authors of the U.S. Constitution had to contend, as well as those who debated the draft presented to them, was the relationship of the states, the original 13 colonies, to the central, or federal, government.  The issue of "states' rights" was deeply intertwined with the issue of slavery, with mostly southern states arguing for the right to make decisions on matters such as this for themselves without interference from the federal government.  The federal government, as it would years later be embodied in the person of President Lincoln, argued, conversely, that the nation could not withstand the kinds of divisions that issues like slavery would inevitably entail, and that the elimination of the institution of slavery was imperative for both the broader nation's moral legitimacy and for the unification of the country.  The threat to constitutional democracy posed by the institution of slavery was such that the federal government felt compelled to force the South to comply with the notion of abolition.  

A federal constitution is intended to definitively resolve such questions. Divisions that existed between the two major regions comprising the newly-established United States of America proved elusive to those charged with debating and ratifying the Constitution, and the Tenth Amendment to the Constitution, ratified at the end of 1791, was an attempt at resolving the issue by declaring that any subject not addressed in the Constitution was left to the states to resolve as they saw fit -- an addition that has definitely concluded the debate about States' rights.  

In conclusion, a federal constitution is the document that, by definition, enjoys the legitimacy of the governed, and that spells out the rights of the governed relative to the government the document is establishing.  It may or may not specify divisions of responsibility, or establish a "separation of powers" between branches of government, as does the U.S. Constitution, but it does set the framework for the structure of the central government while specifying, to the extent possible, the relationship of government to governed.

A federal constitution is one which sets up a system of federalism within a country.  Federalism is a political system in which the national government and the smaller governments (states or provinces) each have their own powers that are specified by the constitution.  In such a system, neither level of government has the ability to infringe on the rights of the other level of government.

In a federal system, then, certain rights and powers are given (by the constitution) to the national government and certain powers are given to the state governments.  The national government does not determine what rights and powers the states have and the state governments do not determine what rights and powers the national government has.  Some federal constitutions give more power to national governments and some give less, but all federal constitutions spell out the power and rights that each level of government has.

A federal constitution, then, is one like the US Constitution which gives specific rights and powers to the state governments and other rights and powers to the national government.