The word "delay" can be used as a verb or as a noun when describing a situation in which something or someone is late. In fact, "delay" has a similar meaning to the adjective "late," but you can’t use "late" as a verb or as a noun.
My flight was delayed for about two hours. (The plane was late. This sentence is in the passive voice. "Delay" is often used in the passive voice.)
I’m sorry I’m late. I was delayed by traffic.
You should expect to be delayed if you drive on a highway where there’s a lot of construction.
They’re going to delay their wedding until next year. (delay = put off; postpone)