Napping comes in many forms. Naps during the first two and a half years are nearly guaranteed. If your child isn't napping and they're in that age bracket, we should talk about WHY they're not napping and how I can help you get naps under wraps! Now... If your child is about 2.5 years old or older and has decided they only want to nap sometimes or never, let's talk about what is happening at that time of day for him/her. There are constructive ways to guide that time to still be as useful as a nap even if your kiddo isn't actually asleep.
One major key thing to remember is that just because your toddler is resisting the nap doesn't mean they don't still need it. If there is anyway to get them to fall asleep to preserve that downtime for yourself, it will benefit everyone involved. It may first start off as shifting nap time to when they're more tired than they had been in the past, or starting nap later but for a shorter period of time.
If they really, truly cannot settle to sleep at all midday, consider letting them experience 1-2 hours in their room to read or play quietly. It is important that you ensure the room is safe (furniture is affixed to the wall, there are no scissors or sharp objects they can reach to play with). Filling up a few bins for them to play dress-up with clothes, read books, or take care of their baby dolls are just a few ways to keep them busy. If you feel the room is not safe for them to be awake and on their own for a long period of time, or if your child is generally not the type to play independently alone in a room, perhaps switch this "chill time" to a living room or a safer play space where you can supervise while simultaneously doing your own thing. Be sure to communicate to them that this is still "nap time" even if they aren't sleeping, and explain what their options are instead of sleeping to maintain a calm and relaxed environment.
How do I know if my toddler is truly ready to stop napping?
He/she is begging to go to do other things when it should be sleepy time... i.e.: needing to use the bathroom more than typical, begging for food, asking you to stay and sing/play/hang out, etc.
He/she is fighting bed time in the evening because of a delayed/late nap.
He/she is able to stay up all day without having a total meltdown in the late afternoon.
If you break free from the nap, you may be surprised to learn that bedtime becomes easier (that is saying a lot for #toddlerlife!!!) On the days my daughter doesn't nap, she is down for the count at 6:30-7:00pm and asleep within 20 minutes. On days she naps (fights it until about 2pm, falls asleep until about 4pm) she doesn't want to go to bed until 7:30-8:00 PM. For parents of two little ones, we need our sacred evening, so if you can keep your sanity by skipping a nap in the daytime, do yourself a favor by skipping the nap and getting that little one to bed at a more reasonable time. Good luck!