The most worthy apology is received with no words but seen with action...
because without action, apologies can’t be heard & are worth nothing
-words from Tyler
Words are nice. They bring instant gratification when spoken from the heart. Hearing something like, "I want to get to know you" or "I'm sorry for the way that I acted. I'll be more mindful in the future," can quickly warm your heart. This is because they create hope and ultimately hope is what keeps us following through with things throughout our lives. If our hope is consistently fulfilled then we keep going. If not, then we eventually leave whatever it is behind. And, that's where action comes into play.
Without actions, words begin to lose their value. For some, words have no value until there is action. Those are typically two types of people: those who let you start with their trust and it's up to you if you break it or keep it. And then those who need you to build up their trust up from the get-go.
Something specific like an apology, as Tyler mentioned, needs a follow-up with action in order for the words "I'm sorry" to truly feel genuine.
If you do something over and over (for example, belittle someone in a crowd of people) and you apologize for it every time but, nothing ever changes, your apology begins to lose value. It no longer feels like you're apologizing from the heart, but instead a formality.
Putting action to your apology (no longer belittling said person in groups of people anymore and instead building them up) is how you gain a person's trust. This is how your words begin to carry weight and positive reinforcement in a relationship - platonic, romantic, family, etc.