When you are arrested, a record of the arrest is kept with the state police. This record is accessible any time a background check is done.
When you go to court, if you are convicted, this becomes a part of your criminal record, which also is accessible when a background check is done.
In the United States, you are innocent until proven guilty. This is the difference between a criminal and police record. You do not have a criminal record unless you are convicted of a crime.
In many jurisdictions, your arrest record is erased when you are acquitted of charges or they are dropped. Your criminal record must be formally expunged or sealed.
Contact your local police department and ask what the procedure is to have your arrest records expunged in your state.