Do iPhone users have the ability to?

My friend once told me that her iPhone has a way to notify her if someone has read a text she sent them. Is this true? I know that there's a send confirmation, but that doesn't always mean the message is received. Anyway, can an iPhone user know if you opened their sent text message?

They can if the phone they are sending a text to has that feature turned on, or they can in imessage

Yes, it's possible while texting through iMessage's in iPhone. That makes you recognize from your end itself, whether the message you have sent is read or not. Hope you find this useful.