What is a covenant?

So on Monday evenings Sarah and I have Family Home Evening (FHE) and we make a treat as well!!  This week we talked about what are covenant's and what not and she was so funny.  She just kept smiling at me and trying to make me happy thinking she was understanding lol!!!!!  It was so cute and I loved her effort of trying.  So at the end of the lesson she and I both made a promise to Heavenly Father that we were going to try and do something better this week!  Sarah says, "I promise to be super nice this week!"  She has not exactly gotten it perfect yet but she isn't even four, I am so happy that she is trying and she wants to make promises with Heavenly Father!  She was super super excited about the chocolate cookies that we made for a treat, we made no bake cookies last week, but she wanted to make the cookies that Grandpa makes!! HEHE!!  Her Nana is to thank for the awesome lessons that we have to do for FHE!