Answer applies to both T and B cells. Briefly? Cross-reactivity (Its Wikipedia page is better ignored).
Slightly longer answer: Clonal expansion and antigen-specific receptors are hallmarks of T and B cells. Tolerance is a developmental process which deletes developing T and B cells whose receptors bind self-antigens with strong affinity. Following this critical checkpoint, mature T and B cells circulate within the body. Per textbook definition, each of these T and B cells bears a unique receptor that binds a unique antigen. That’s certainly true but only partially so. Cross-reactivity is the piece that completes it.
Cross-reactivity means each unique T cell (TCR) or B cell (BCR) receptor has the capacity to bind a range of related antigens, i.e., it’ll bind some of them with very high affinity, others with much lower, but bind them all it will. This is the adaptive immune system’s way of hedging its bets to ensure that circulating T and B cells can more or less bind whatever antigen comes their way. In other words, TCRs and BCRs are promiscuous, capable of binding more than one antigen. Scope for cross-reactivity is much more vast in the case of the T cell since its receptors don’t directly bind an antigen but rather only a tiny piece of it, the peptide epitope, presented within an MHC molecule (See figure below from 1).
Similar principle applies to B cell receptors (BCRs) (See figure below from 2) and their antigen-binding sites,.
1. Sewell, Andrew K. “Why must T cells be cross-reactive?.” Nature Reviews Immunology 12.9 (2012): 669-677.
2. Kieber-Emmons, Thomas, et al. “Carbohydrate-mimetic peptides for pan anti-tumor responses.” Frontiers in immunology 5 (2013): 308-308.