If your parents have not been especially involved in a religion, then they may rely more upon you and others to help them make peace with certain issues. As we age, we may feel an increasing need to feel that our life mattered, that somehow we made a difference. Elderly persons may often be found simply sitting and staring off into space. This may actually be an involvement in a life review, i.e., a summation which they are undertaking to be at peace with the quality of their life. If your parent chooses to share any of this with you, be a good listener.
Some elderly persons feel some urgency in making amends.
If this involves you in any way, the best that you can offer is honesty. If you harbor hurts from a parent trying to make peace with you, be honest. Perhaps the best you may be able to offer is to tell you're parent that you appreciate them reaching out and that you are willing to work on forgiveness. As we age, we also come face to face not only with our mortality but with our beliefs about an afterlife. Again, the best that you can offer is listening.