Regular expressions are strings that define patterns to match character sequences. They can be used in Cisco IOS show commands and AS-Path access-lists to match BGP prefixes based on AS-Path information. Regular expression characters have specific meanings, such as ^ and $ to match the start and end, [] for ranges, and * + ? for quantity. An example expression matches routes originated from directly connected ASes or their customers by representing AS numbers as "X" and using quantity symbols to account for multi-digit ASNs.