This is a polite way to introduce two people to each other. First you say the first person's name. You start with the person you were just talking to. In this example, you were talking to Jeff but you said "How rude of me!" to Karen, so you start:

Karen,

Then you say "this is" and then describe the relationship:

this is my sister's husband

this is my colleague

this is the president of the University

And finally you say the second person's name. In casual situations, you can give just a first name. In more formal situations, you give first and last name.