What are VoIP, Callthrough and Callback anyway, and how can those services be used for making cheap international phone calls?

Here, we have compiled a list of explanations of various terms that describe how our service works:

1. Call-by-Call
2. Calling Card
3. Callback
   
4. Callthrough
   
5. Fritz!Box
6. NGN
7. Provider
8. Realtone
9. Roaming fees
   
10. Smartphone
11. VoIP (Voice over IP)