Frist means a period of time, a term. In English, we say “one month’s notice, said notice to expire at the end of the month.” In other words, you must give notice at least a month in advance, and the notice is considered to be given on the last day of the month in which you give it. If you gave notice on, for example, April 3rd, for example, the notice would be accepted on April 30, and the change would not be effective until a month later, i.e., on May 31st / June 1st, depending on the contract and local custom.