When you apply for asylum in a country of the European Union, there is a procedure to decide which country is responsible for your asylum claim. This is not necessarily the country where you applied for asylum. This procedure is called the "Dublin Procedure" and the countries that take part in the Dublin Procedure are called "Dublin countries". There are certain criteria under which a country can become responsible for your asylum claim. For example, the country where you entered the European Union or the country where you first made an asylum claim can be responsible for your asylum request. There are also other criteria, such as having close family members in another Dublin country. Here you can find more information about the Dublin procedure: https://www.mobileinfoteam.org/dublin-3
If you apply for asylum in a Dublin country, your fingerprints will be checked within the Eurodac system to see if another state might be responsible for your asylum claim. If the authorities will find a match in the Eurodac system, they might, depending on your individual circumstances, ask the other state to take you back. Also, if you are caught by the police without having a legal permit to stay, the police will check your fingerprints in the EURODAC system to see if you have already applied for asylum in another state.
Here you can find more information about fingerprints: https://www.mobileinfoteam.org/fingerprints