STR markers are "short tandem repeats" - segments of DNA (2-13 nucleotides in length) which are repeated multiple times. Y-DNA STRs are the STRs that are found only on the Y-chromosome (male chromosome).
STR analysis measures the exact number of repeat units. The number of repeats differs between individuals because STRs change frequently. The more closely related two individuals are along their direct paternal line, the more similar their Y-DNA STR profiles will be.