In the federal system citizens participate in the government on different levels like nation, state or local elections. In a unitary system the most power is usually held by the national government which citizen don’t have that much influence over so they go more towards central government. Lastly in a confederation system, most power is held by states so citizens influence their state government more than national.
Division of power means the authority is shared between different levels of government. In the u.s. the federal government handles national issues like immigration and state government handles education. These prevent from power being over powered in one place.
The federal government influences state or local governments through things like funding and policies. For example during Covid the federal government influenced nyc by setting public health guidelines through cdc. The cdc was able to issue rules on wearing masks, social distancing and safety regulations to help slow down the virus.