This is an episode from The Big Bang Theory, a "sitcom" (situation comedy show) in the US. Although it is an old episode, the vocabulary and phrases are still useful and colloquial. The humor is also cultural. Some jokes you may find funny, while others you may not.
One of the funny parts in the show for learners of English in Taiwan may be when the character Sheldon is learning Chinese. His purpose for learning Chinese is simple - to argue with the manager at a local Chinese restaurant about their style of chicken, a popular dish in the US called "Tangerine Chicken." As tangerines have a slightly different taste from oranges, Sheldon argues that their "Tangerine Chicken" is really "Orange Chicken." It's supposed to be funny because Sheldon likes to argue about meaningless details.
Here are some phrases that will help you. Try to watch several times until you can hear all of them mentioned in the show.
*NOTE: Do not use the subtitle option for this video. The subtitles are all incorrect! Not my video...
1. As the teacher, it is your job to separate your idiosyncrasies from the subject matter. - idiosyncrasies are a person's unusual behavior
2. Once you’re fluent, you’ll have a billion more people to annoy instead of me. - to annoy means to bother
3. I believe the Sechuan Palace has been passing off “Orange Chicken” as “Tangerine Chicken, and I intend to confront them. - to "pass off A as B" means to replace B with something fake, A. "to confront" means to talk to someone about a problem that he or she caused.
4. The relationship was broken beyond repair. - A common phrase that means the relationship could not be fixed.
5. I thought the first two renditions were far more compelling. - a "rendition" is a different version of a story or song. "compelling" means exciting
6. That’s the spirit! - We say this when someone shows high enthusiasm. (Here it is used ironically. She doesn't really show enthusiasm.)
7. Why don’t you just pick one at random? - to "pick one at random" means to choose any one you want without making a judgment
8. Sorry, you diverted me. - to "divert" someone means to take someone's attention away
9. Schroedinger’s Cat Theory - This is a real theory in Quantum Mechanics. You can read about it here. Schroedinger's Cat Theory
10. I don’t get the point. - to "get the point" means to understand the most important part of a discussion - to "make a point" means to say that important part out loud.11. Tell me whether or not to go through with the date. - to "go through with" something means to complete something you promised to do