do

[mak]

I do know that ...
I do understand that ...

Why is 'do' used in these sentences?

[Robbie_Durham]

They would work perfectly well without "do". It's just an extra word in those sentences. I suppose though, that it does help to show that you know what you're saying.

[Bota Tamara]

I think that 'do' in those centeces is used to make the centence stronger.
I know the lesson = I learned it
I do know the lesson= I learned it very well

[rewboss]

I'll have to disagree with Robbie; it is not just an extra word.

This construction is used in two different ways:

1. It contrasts the positive sentence with a previously negative sentence; for example:

A: "Look, you obviously don't study hard enough."
B: "I do study hard -- really, I do."

"I don't know much about history / Don't know much biology / Don't know much about a science book / But I do know that I love you..." (Sam Cooke, Wonderful World (Don't Know Much))

2. For emphasis:

"I do wish you'd wash your ears out!"

This puts a certain kind of emphasis on the sentence. You could instead just emphasise "wish": "I wish you'd..." -- but this is an alternative, and native speakers often use this construction to add a very subtle kind of emphasis.