In business today, the handshake is used as a worldwide gesture for meeting, greeting, and sealing a deal. It is a ritualized gripping of another's hand, with one or more up-and-down (or, in Texas, sideways) motions followed by a quick release. Since the fingertips and palmar surface of the hand are exquisitely sensitive, the shake itself can be deeply personal. We instantly feel the warmth or coolness, dryness or moistness, and firmness or weakness of another's grip. Sensory input from a hand's thermal and pressure receptors to the brain's parietal sensory area can be intense (especially in courtship). From the parietal lobe, the handshake's message travels to deeper areas of the limbic system for an emotional interpretation to judge how the shake felt.
If you travel to France on business, be prepared to shake hands dozens of times a day. Office workers in Paris may shake in the morning to greet, and in the afternoon to say goodbye, to colleagues. Outside vendors and technicians will handshake with everyone present when they enter or leave an office. Contrast this to the Japanese practice of giving few intra-office handshakes in favor of polite bows of the head. In Islamic nations, it is strictly taboo for men to shake hands in public with women. So, while the handshake has become a worldwide gesture in business, you should learn cultural protocols on shaking before you travel.
Since in much of the world a handshake is both a visual and a tactile index of your concern for other people, a rule of thumb is not to hold back. In North America, Latin America, and Europe, take the lead, step forward, and shake a hand. Shaking will raise your extrovert quotient and show colleagues you care about them as people. In Asia, South Asia, and the Middle East, handshaking may be more nuanced. Learn the cultural rules in these regions before stepping forward with your hand up-and-out. An Asian namasté, with your palms and fingers pressed together in front of your chest, given with a slight bow; or a Muslim salaam, in which your right hand touches your forehead, also with a slight bow, may be better signals to send.
Wherever in the world you conduct business, don't hide your hands in the background or keep them out of sight. Show them to attract notice to yourself and to emphasize your ideas. Hands are great ambassadors to those in business you don't know well. In their unspoken language, which is both mysterious yet understood by all, hands speak strongly on your behalf.