go above and beyond (the call of duty)

This is a set expression. To "go above and beyond the call of duty" means to do a lot more than you are required or expected to to for your job. If you break the expression down into parts, "go above and beyond" means to do more. "The call of duty" means "the things that you're asked to do for your job". This expression comes from the military, where it was used to talk about soldiers who died while fighting for their country.

Now, the phrase is often used to talk about teachers, social workers, nurses, and other people who work hard to help people. It can also be used to talk about customer service:

We go above and beyond the call of duty to ensure that every customer is 100% satisfied.

As you can see from the example at top, you can also leave off the second part and just say:

They really go above and beyond.

Whether you include "the call of duty" or not, this is a pretty formal phrase. It fits best in written English or in formal speeches.

deliver (something) to (students, customers, readers, etc.)

You probably already know that "deliver" is used as in, for example, delivering a pizza. But it can also be used to talk about giving something valuable to your students, customers, readers, listeners, bosses, and so on. This isn't usually a physical object. It's usually some kind of feeling or idea. For example:

PhraseMix delivers realistic English phrases that you can use in day-to-day life.

Our job is to deliver an entertaining and relaxing experience for our guests.

My methods can be a little disorganized, but I deliver results.

the very best (something)

The phrase "the very best" is just a stronger way of saying "the best". It's a sign that the person is not talking about the top 20% of something, but maybe the top 5%. For example:

The secret to our success is that we only hire the very best people.

In this sentence, the speaker wants the listener to think that they hire the most qualified employees, with a good educational background and a lot of experience.

If I'm taking my wife out for dinner at a really nice restaurant and she acts surprised, I might say:

Only the very best for you, my dear.

This would be a joke, because she knows that we don't always eat at such expensive restaurants.

each and every (something)

"Each" and "every" basically mean the same thing. But people use them together in the phrase "each and every" when they want to emphasize the idea of "every" or "each". It's also a little more common in speeches to large groups of people than in one-on-one conversation. For example, you can say this to a group of employees:

I want each and every one of you to come up with a list of five to ten potential customers. Who should we be pitching this to?