SMS was free when I started using WhatsApp, but MMS wasn't, so I think that was part of why it took off in the UK. You could finally send pictures and videos and have read receipts and typing indicators and group chats. Plus it was instant and reliable where SMS always felt slow and unreliable.
Also it worked on WiFi so you could still use it at home where you might not have had the best phone signal.
It became popular when you had to pay for it. It was a one off fee on iPhone or an annual recurring fee on Android, that's how much people wanted to get away from SMS.
Probably worth noting that BBM was very popular at that time too but it was exclusive to BlackBerry phones so the concept wasn't new, but everyone that started moving to iPhone and Android after blackberry wanted the same messaging experience, and WhatsApp provided that.
I'll never really understand why the north American market didn't make the jump like everyone else did, because WhatsApp provided so much more, it wasn't just about cost of messaging.