Business etiquette rules for introducing people in a business setting are not much different from the accepted customs of personal introductions in a social setting. Unfortunately, the rules of introduction are not so straightforward and simple as one might think, and who you introduce first does matter
An Outdated Business Rule – Only Introduce Men to Women
Situations Where Social and Business Introduction Rules Are the Same
In both business and social situations, you should always introduce:
 Younger people to older people;
 Junior ranking professionals to senior ranking professionals;
 Business contacts and staff to clients;
 Personal acquaintances and family members to business professionals when attending a business function; and
 Guests to their hosts.

In other words, as a show of respect introduce those of a lower status to those of a higher status whether it that means a social or professional status. As antiquated and unfair as this may sound, this protocol for introducing people is still considered socially acceptable (and often expected) in the U.S. and many other countries.

Differences Based on Discriminatory Practices are not Status Indicators
It is important to note that under no circumstances should you use introduction rules to socially define people of another race, color, religion, or sexual preference as a someone of a lower status. To do so would be purely inappropriate and discriminatory.
The purpose of "designed" introductions is to show respect for presumed social order based on position or accomplishment, and not to demean or "classify" other people as being inferior.
Social Protocol for Introducing People in a Business Situation
In a business setting, always introduce people by saying their title and full name first, and then follow with a brief interesting or relevant piece of information about the people you are introducing.
Example: When introducing Sally Rider, one of your advertising and marketing managers, to Dr. Jennifer Wilkins, a business client, you introduce Sally (a subordinate employee) to the senior professional (in this case, the client):
"Dr. Jenkins, this is Sally Rider, our top advertising and marketing executive who will be personally handling your account with us. Sally, this is Dr. Jennifer Wilkins. She heads the women's education department at the Advanced Institute for Business Women. Dr. Wilkins is interested in new ways to market their education programs to women."

If the person you are introducing has no title, you do not know their title, or it would seem too formal for a particular setting, you can offer their name first, but still followed with information about what they do:
Example: This is Margaret Dixon. She heads up the new software development team at ABCDE, Inc.

How to Respond to an Introduction
When someone has just been introduced to you, your response should be genuine, short, and simple. You should also should repeat the person’s name at the end of your greeting.
Repeating the name of the person you were just introduced to serves two purposes: it shows polite respect and it helps you to remember the person’s name. You can also add a brief comment about the person (not about yourself):
Examples:
”It is so nice to meet you, Dr. Wilkins. I have followed your work for years with much enthusiasm.”

”It is wonderful to finally meet you, Dr. Wilkins. I look forward to working with you.”