She is only the second woman ever to ascend to the Secretary of State's position, so in that way, she is a pioneer for other women wishing to run key positions in government. She is arguably the woman who came closest to being elected President, and served notice that a woman President is probably going to be elected in the near future. That's not to say she's inspiring to every girl, as she is also a very controversial figure and people seem to tend to like her or hate her, much like her husband.
If Secretary Clinton does hold inspirational value, it would lie in her "18 million cracks in the glass ceiling" notion. Prior to her 2008 bid for the office of the President, a woman had not been able to launch a successful and serious campaign. Secretary Clinton did that in her challenge for the Democratic nomination. She did inspire many with her ability to appeal to voters across lines of gender, class, and personal experience. Another way she can be seen as inspirational would be through her time as First Lady. An argument can be made that she was influential as a First Lady on both the position and its capacity for legislative influence. Her role in the health care debate in the early 1990s invoked many of the same principles seen in the current health care debate. At the same time, her loyalty to her husband, the President, during the latter portion of his tenure can be seen as inspirational.
There are a number of things about Hillary Clinton that is inspiring. First, she ran for the nomination as president as a woman and she nearly won. This fact alone is inspiring. One could say that she is breaking tradition by doing this and young people usually like the idea of breaking tradition. Second, she had gone through a lot of difficulties with her marriage and yet she remains faithful. Irrespective of what one thinks of this, there should be a level of respect. Finally, she is an intelligent person with great drive.
Hillary Clinton is a role model in a number of ways for all of us, not just for teenagers. In the face of the public humiliation of her husband's behavior and the loss of the Democratic nomination for the presidency, she has held her head high and conducted herself admirably. Many women in her situation might have retreated from public life. Or, as a top-notch attorney, she could have chosen to go into private practice again or to join her husband on the speaking circuit for her own personal gain. but she has chosen to use her intelligence and energy for the public good. In today's political environment, there are many skilled, intelligent people who do not want to become public servants because the exposure is so hideous, not that I can blame them, but the fact that Hillary Clinton has chosen to continue to serve is an inspiration.
For teenagers in particular, there are a few important messages. One is that staying in a marriage that is not perfect is a viable option. There are few examples of that today. Another is that one can experience a defeat and still have experience success. There are second acts in American lives!
Your question, of course, assumes that she does inspire young teenagers. This may be true of some, but it is certainly not true of others, particularly among conservative Americans.
To the extent that Hilary Clinton does inspire young teenagers, it is likely to be because of the fact that she has done at least one thing no other woman has done before. Mrs. Clinton was the first woman to be a serious contender for a presidential nomination. She now holds a high position (Secretary of State) in the Obama administration and that might make her an inspiration as well.
Hillary Clinton has long been a role model for teens. When Mrs. Clinton ran for the presidential office sales of teen sized pants suits and dress shoes increased inspired by the Hillary Clinton look. One of the most important ways in which Senator Clinton has inspired teens is that she has shown them that it is not a remarkable that a woman in America can run for the highest office in our country. She has been a leader in every avenue that she takes. One political area that she has helped to champion has been in education reform. She has helped to set-up programs that help to decrease teen pregnancies. Her own daughter is evidence that she can be a good mother, a politician, and a leader. Even in her concession speech, she demonstrated to the teens that honor and dignity should rise above the taste of defeat.