Glycopeptides work by inhibiting the synthesis of peptidoglycan, which is a critical component of the bacterial cell wall. By binding to the D-Ala-D-Ala terminus of cell wall precursors, glycopeptides prevent the cross-linking of peptidoglycan chains, leading to cell lysis and death. This mechanism makes them particularly effective against methicillin-resistant Staphylococcus aureus (MRSA) and other resistant strains.