First Example:
Rachel: How was your weekend?
Charlene: Fantastic! Tom took me to a really amazing restaurant, and then we went for a walk on the beach.
Rachel: Aww! That sounds so sweet!
Charlene: And then the best part - he finally said those three little words I've been waiting for.
Rachel: Wow! So you guys are really getting serious!
Charlene: I think so.
Meaning: The expression "those three little words" refers to the phrase "I love you." Since "I love you" is considered such a strong and powerful thing to say, we often use the phrase "those three little words" to refer to the phrase in conversation. Usually, this is used when at least one person in a couple hasn't said it to the other, but it can also be used for the first time one partner says "I love you" to the other, as in the above example. In this example, Charlene is excited because Tom finally told her that he loved her.
Here is another example:
Dale: How are things going in your new relationship?
Colby: Pretty well. I can't believe we met online.
Dale: How long have you guys been going out?
Colby: A little over a month.
Dale: Wow! If you don't watch out, someone's gonna slip up and say those three little words!
Colby: It wouldn't surprise me. I'm actually really happy
Dale: Glad to hear it. You two seem like a really great match.
In this instance, Colby says that his new relationship is going really well, and Dale jokingly warns that someone is going to slip up (which means "make a mistake") and say "I love you" to the other. This expression is often used in contexts such as this, when a relationship is getting serious but no one has said "I love you" to the other person yet.