DD didn't toilet train until 3.5. I tried earlier but she just didn't get it. We gave up and went back to nappies. A few months later I asked her if she wanted to wear undies instead and she said yes. She had plenty of accidents but she seemed to grasp the idea much better. However, it took about 6+ months for her to get poos sorted. It was a nightmare. She just did not want to poo on the toilet. She finally got into the habit of doing it on the toilet before bath time and then she got used to pooping in the loo. She'll be 5 in Aug and she still occasionally has wee accidents (mostly because she waits too long and doesn't want to stop what she's doing) and she still wears a night nappy.
DS is 19mo and I can't even imagine starting at this age, I just don't understand how a kid this age could toilet train!! But his language isn't well developed yet and he only just started walking so he's nowhere near ready. Unless he shows really strong signs of wanting to TT, I won't even attempt it until about 2.5/3yo.
Some kids just take longer. It's a simple thing for some kids, but for others it can be a real challenge.