(name), this is (relationship)(name)

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.

take over (a job or position)

When someone "takes over" a job, it means that the person who was doing the job before stops, and the new person starts.

We often use the phrase "take over for (someone)":

She's going to take over for you while you're out on maternity leave.

You can also say "take over as (the name of the position)":

I heard that you're going to take over as head coach starting next season. Congrats!

Finance

"Finance" is an area of business. It's a part of business that deals with money.

"Finance" is a little different from "Accounting", which is another job that deals with money. Finance is about raising money, figuring out how to invest it, and so on. An accountant is mostly concerned with recording and calculating business expenses.