During her 2008 campaign for the Democratic Presidential ticket, one of the primary criticisms directed towards Hillary Clinton's was that she had difficulty connecting with people emotionally. Indeed one moment where she enjoyed a surge in the poles was after her eyes welled up with tears during a "town meeting" type gathering in Portsmouth, New Hampshire. This act made her "feel more human" to the common person. It transmitted more sincerity and made her more emotionally accessible. In short this one act increased her rapport to the masses.
President Clinton was and still is a master at building rapport. Even staunch republicans will be enamored (for a while) upon meeting him. One of the many ways Bill builds rapport is within the context of his handshake. While he will shake fewer hands per minute during any given gathering compared with most other politicians - he connects more deeply with the emotions of those he does greet. So even if you don't get to shake his hand and exchange five or ten words with him - watching others do so (even if on a news video) will help build his rapport with you. Never forget - watching a sincere interaction engenders the same experience in others - by surrogate.
A key component of President Clinton's handshake (but certainly not the only one) is how he points every part of his body during the handshake. Note in this photo, Hillary's feet (although not seen directly) are not pointed at the man whose hand she is shaking. Neither are her hips. And her shoulders are also not square to him. Never mind that he's not doing so - in order to gain the maximum rapport and make a person feel, if only for a few seconds that they are the only person in the world of whom we are thinking, the feet, hips and torso should always point directly at them. Hillary is omitting this crucial communication component. Moreover, when the rest of the body is pointed away we must turn our head and/or eyes in order to look at them - as are hers. This "non-direct" gaze gives them the feeling they are not respected, not trusted, not valued and/or not believed.
Also notice carefully a component of Hillary's expression - her eyes are opened wider than baseline in a pseudo-surprise expression. During a sincere smile (Duchenne smile) the eyelids are partially closed in a very particular fashion - with a temporary coexisting concave-up furrow in each lower lid. The lack of these specific eye findings signals the existence of a false-smile. This is not to say that Hillary Clinton, another politician, you, I or any other person is "insincere as a whole" (e.g. the whole personality) - however it does indicate that in that moment she (or anyone else who expresses this or any other of the numerous varieties of non-sincere social smiles) is having to push out a less than sincere expression. People feel this false sincerity. They don't describe it in psychological bullet points, but they feel it none-the-less.
Negotiation Body Language Secret # 441: Bill Clinton's Rapport and His Temporary Universe
Nonverbal Communication Analysis # 2360: Bill Clinton and the Body Language of a "Loose Hand, Palm Up Point"
Nonverbal Communication Analysis # 2379: Bill Clinton's Speech at the George W. Bush Presidential Library Opening Body Language of Former and Current President
Nonverbal Communication Analysis # 2128: Mitt Romney's & Bill Clinton's Body Language during Mitt's Joke at 2012 Clinton Global Initiative
Negotiation Nonverbal Communication Secret # 1499: Bill Clinton's Empathy for Eric Fehrnstrom and Mitt Romney ... What's Your Sincerity Quotient?
Nonverbal Communication Analysis # 2126: Bill Clinton on whether or not Hillary will run for President in 2016
Nonverbal Communication Analysis # 2125: Presidential Debate Body Language - George H.W. Bush, Bill Clinton and Ross Perot 1992