The United States is a very good example of federalism. Federalism is a system of government in which there are lower levels of government (we call them states) and a higher level of government (the federal government). Each of these levels of government has its own powers that are set out in a constitution. The federal government cannot take away any of the rights given to the state governments. The state governments cannot take rights away from the federal government.
The major implication of federalism is that things will be done differently in the different parts of a country. For example, in the United States, people have different rights depending on what state they live in. A person who lives in the state of Washington has the right to a same-sex marriage while a person in Idaho, which borders Washington, does not. Different states also have different laws on such things as the death penalty or income taxes and on much less important things such as speed limits.
When a country has a federal system, people in the various parts of the country will end up having different rights and somewhat different laws.