Concurrent powers are those powers which are given both to the national government and to the state governments. These can be exercised separately by the two levels of government. Two important examples of this type of powers are the power to tax and the power to build roads.
The federal government and the state governments both have the power to impose taxes on the people. This is why we have federal and state income taxes in most states. Both levels of government have the right to build roads. This is why we have interstate highways but also state highways.
These are the two most important concurrent powers.