As a daily WhatsApp User myself, here are the reasons why I prefer it over other similar messenger services:
1. It's the facebook of messengers (now it's just facebook...). In most of Europe an Africa there's a 90% chance , that your friend with a smartphone has also WhatsAp installed. Even the older generation (40+) uses it frequently. In Africa, they even have a song about it [1].
2. Cross-Platform: It's available on most common smartphone platforms and looks almost identical across these. There are no hassles of sending stuff (videos, locations) across these platforms. Changing your smartphone is not a problem as long as you keep the same number.
3. It feels snappy: In comparison to iMessage, FB Messenger it's fast and has no disturbing gimmicks. You see messages instantly and it feels like a chat when iMessages feels more like bloated sms...
4. It works in places with unreliable network like rural regions. iMessages fails here often, FB apps also need a stable connection to work properly.
5. A few years ago unlimited text plans were not as common as in the US. Because of this people looked for an alternative to paying ~19c per text (EU). WhatsApp was one of the most polished solutions with a low entry barrier.
[1] http://www.youtube.com/watch?v=zaFkpVrC2sw