Lauren Cooper is a fictional character in The Catherine Tate Show. She is a comprehensive school student with a surly attitude and was most widely known for her phrase "Am I bovvered?" (i.e. bothered - the "v" in the word takes the place of the "th" that should be there). When feeling angry or embarrassed, she frequently replies with defensive responses such as "Am I bovvered?", "Do I look bovvered?" or "Are you disrespecting me?", among others.
Both the physical appearance and the behaviour of Lauren and her friends are mock stereotypes of the Chav subculture. If you don't know what chav means, look it up here: http://self-learning-eoicoruna.blogspot.com/2008/10/word-of-week-27-october-2-november-2008.html
Despite Lauren's blatant disregard for authority, and chav-like demeanour, she sometimes shows surprising intelligence. She is well-versed in the Periodic Table, she apparently knows Shakespeare and she is fluent in French (once surprising her French teacher by asking her "Regardez mon visage. Suis-je bovvered? Est-ce que vous appelez ma mère une Pikey?"), although she refuses to speak it for an oral exam.
In 2006 Tate's catchphrase "bovvered" was named Word of the Year and was poised to enter the Oxford English Dictionary. A spokesperson for the OED commented: 'Am I bovvered?' and its follow-up, 'Does my face look bovvered?' had already come to be seen as the perfect expression of a generation of teenagers and their speaking style."
Some notes to help you understand the two sketches: