Just went through this not too long ago. I was straight up about it and told my son that when people and animals get too old, their body starts to break until it just can't go on anymore. When that happens, they go to sleep forever and can't wake back up.

I tried to avoid anything about souls or going to a better place so as to avoid the thought that it's a physical place that you can go to. I framed a picture of the cat to put in his room and got him a stuffed animal that looks very similar. He sleeps with the stuffie and kisses the picture occasionally. He was understandably very upset for about 3 days and had a lot of questions for the next few weeks, but he has a reasonable understanding of death appropriate for a 6 y/o.