It's an honor to (do something)

When you get special recognition or a special opportunity from people that you respect highly, it's "an honor". You can use this phrase in sentences like these: 

It's an honor to meet you.

It's such an honor to be invited to speak to you all here today.

I don't even care if I win. It's an honor just to be nominated!

This phrase is rather formal. When you use it, you sound very thankful and humble.

truly

The adverb "truly' means "very much" or "honestly". You can use it before an adjective like this:

I'm truly sorry for what happened.

The most common adjectives that follow "truly" are:

• truly great
• truly remarkable
• truly amazing
• truly sorry
• truly happy

You can also use "truly" with a verb:

I truly forgot all about it.

I truly believe that you will achieve your dream some day.

"Truly" is pretty formal.

someone of (your/his/etc.) stature

"Stature" means "importance" or "status". We use it in the phrase "someone of (his/her/your/their) stature" to talk about people who are very highly respected.

I wouldn't dare ask such a favor from someone of her stature.

The original meaning of "stature" was actually "height", so you can imagine that a very important person seems metaphorically taller than others.

(someone) has influence

A person who "has influence" is able to affect or even control a lot of people or events.

Someone might "have influence" because they're famous, becuase they're wealthy and well-connected, or because they're well-known in a certain field.

When you're describing someone who "has influence", you can also say that they're "influential".