Requirement is something you need to do to be compliant with the standard. It is essential if you want to be certified against the standard. Requirements are listed in clauses 4 to 10 of the main part of the standard.
Controls are practices or technologies, you need to implement to: reduce risks to acceptable levels; fulfill legal requirements (e.g., laws, regulations or contracts); or fulfill a top management demand. Controls are listed in Annex A
This article will provide you further explanation about how ISO 27001 works: