I don’t think classic SMS does this, but RCS and IMessage both do. SMS has ‘delivery reports’ (ie, the carrier will let you know when they succeed in transmitting it to the phone), but not actual read receipts.

As a sender; sometimes a message doesn’t warrant a response, but it’s nice to know it was actually received/seen.

As a recipient though, I’ve always found it a tad creepy and turned it off on every phone I’ve had.

There once was a frog named Kermit, who dated Mrs Piggy, and every other wednesday night they get bizzy…