“She did tell some interesting anecdotes, though.”

You went to a talk last night. You are describing the speaker and the event to a coworker who wasn't there. You were just criticizing the speaker for not being interesting, but you don't want to sound too negative about the event. So you say:

She did tell some interesting anecdotes, though.

(something) did (happen)

In a normal sentence, you don't include "did" before the verb:

She told some interesting anecdotes.

But when your sentence is contrasting with something else that you just said, you should use the word "did" and place a strong stress on that word when saying it:

I didn't think he was that good-looking. I did like his hair, though.

In the example above, you're contrasting this positive statement about the speaker with your earlier negative statements.

tell an anecdote

An "anecdote" is a story that you tell as part of a speech or a talk. An anecdote usually makes a certain point in an interesting way.

though

"Though" is similar to "but" and "however". It is usually used at the end of the sentence in spoken English:

I have a pilot's license. I haven't flown in almost 5 years, though.

In written English, it's more appropriate to use it between clauses:

I have a pilot's license, though I haven't flown in almost 5 years.

"Though" is more casual than "however", which can be used in the same way:

I do agree with the Prime Minister on defense, however.