What is a federal constitution?
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.