"Laid off" = the company/factory is short of orders, does not have enough work for its staff, is in some kind of financial difficulty, so lays off [ = sends them home] a percentage [hopefully with pay] of its workers with the hope that they will be re-employed when things improve.
"Fired from" = the worker's employment has been permanently terminated. He is no longer employed by the company. It is a negative term, implying some form of wrong behaviour or action by the worker.
Student or Learner