To “brainstorm” (brainstorm) means to make a long list of ideas, usually in a group with other people.

“Brainstorming” means that everyone tries to come up with an idea, and you don't talk about the ideas right away; you write them all down, and then you talk about them.

Brainstorming is a good way to get a lot of creative ideas, and then later people decide which ideas are good and which ideas are bad.

So when Chris says, “In a minute, we're going to ask you to help us brainstorm even more ideas,” he means that soon he's going to ask the people in the room to be creative and to try to think of new ideas.

Chris then says, “Before you get your creative juices flowing, let's just briefly recap the main points of the presentation.”

To get one's “creative juices (juices) flowing” means to begin to think creatively, to begin to think of new ideas.

Some people get their creative juices flowing by playing games or reading a book.

The word “juice” (juice) usually refers to something that is liquid, such as orange juice.

To “flow” means to move, so getting your creative juices flowing means getting your ideas and being creative.

Chris means that he wants people to think creatively while they're sharing ideas, but first he wants to recap the main points.

To “recap” (recap) means to review or to summarize something.

“Recap” is short for “recapitulate”: to review; to repeat; to summarize.

As I said before, in an U.S. presentation it's expected that you will recap, or repeat and review, your key points so that people in the audience, listening and watching, will remember them better.

In your classes, when you were in school, your teacher probably recapped the main points of the lesson before the class ended.

Chris says that the company's market share has been taking a beating.

To “beat” (beat) means to hit something hard, so to “take a beating” means to be hurt - someone else is hitting you; you're being defeated or losing.

You could be, in this case, losing a lot of money.

The company is losing money; it's taking a beating.

A car, for example, takes a beating during an accident.

You can invest money in the stock market, and if your stocks go down (if the price of the stocks that you bought go down), we would say you took a beating in the stock market - you lost; you were defeated.
In this case, the company has taken a beating, meaning it has been hurt because it has lost market share.