First, we must note the difference. The federal system used under the USA allows the government to be branched, so that each area of the land is allowed to focus on their own problems, with a general government to help enforce, supply, and be the 'parent' of the smaller governments. In this way, it eases the tasks needed for a central government, which in turn can focus on national interest and over-sea policies. This type of government also has three branches, and with the passage of the checks-and-balances, allows the three to share equal power and to make sure that none of the branches become to powerful (in becoming a unitary government).
In a unitary system, however, the central government (national) is the only power and only gives its power to those they wish to have. The country is only governed by one branch, the executive branch, which also incorporates all other branches together too. However, there are many sub-branches, but they do not have the same rights (as they do not have checks-and-balances, as in the federal system). These rights are given by the central government, who has the final say in all things.
hope this helps