sincere

An honest person has sincere feelings or intentions.

When someone says they feel sorry for what happened, and you can tell they really mean it, that's an example of sincerity. Imagine you've lost your favorite book, and a friend offers to replace it with a new one – if they say it was their pleasure to do so, without expecting anything in return, that's sincere. Sometimes people use the word sincerely when signing a letter or message, like "Sincerely, John" at the end of an email. In this case, they're promising that everything written is true and genuine.