A highly specific antibody will exhibit minimal cross-reactivity, meaning it will bind only to its intended target antigen with high affinity and selectivity. In contrast, an antibody with high cross-reactivity may bind to multiple antigens, including those with similar epitopes, exhibiting lower specificity. In assays, specificity is significant as it ensures accurate detection of the target antigen without interference from nonspecific binding. High cross-reactivity can lead to false-positive results by binding to unintended antigens, thereby impacting the specificity of the assay.