A promoter is a DNA sequence that can recruit transcriptional machinery and lead to transcription of the downstream DNA sequence.
The specific sequence of the promoter determines the strength of the promoter (a strong promoter leads to a high rate of transcription initiation).
In addition to sequences that “promote” transcription, a promoter may include additional sequences known as operators that control the strength of the promoter.
Sometimes, we ignore the details of how a promoter works and think of a promoter as a device that converts inputs into outputs. You can do this when designing a multi-component system that includes promoters whose activity must be regulated by other species in the system.