The process of transcription, is influenced by the interaction of proteins called transcription factors (TFs) that bind to specific sites called Transcription Factor Binding Sites (TFBSs), which are proximal or distal to a transcription starting site. TFs generally have distinct binding preferences towards specific TFBSs, however TFs can tolerate variations in the target TFBS. Thus to model a TFBS, the nucleotides are weighted accordingly, to the tolerance of the TF. One common way to represent this is by using a position weight matrix (PWM), also called position-specific weight matrix (PSWM) or position-specific scoring matrix (PSSM), which is a commonly used representation of motifs (in our case TFBS) in biological sequences.
How do we find TFBSs? DNA sequences that interact with TFs can be experimentally determined from SELEX experiments. Since this process involves synthesis of a large number of randomly generated oligonucleotides, DNA sequences that interact with TFs can be determined, as well as the tolerance at specific sites. From SELEX experiments, a position frequency matrix (PFM) can be constructed by recording the position-dependent frequency of each nucleotide in the DNA sequence that interacted with the TF. Here's an example of a PFM as shown in this review "Applied bioinformatics for the identification of regulatory elements" (sorry paywall!):