If you're asking how a computer sends a text to a phone
The software is connected to a system that has an assigned phone number. When you send a message, the software handles it the same way your phone sends a text using it's assigned number. The recipients phone doesn't know (or care) how the message originated.
With everything being IP, there's not much difference between your smartphone and a "computer".
DonKarnage1 t1_itzgu8o wrote
Reply to eli5 how does the technology work that allows a computer software to send text messages? by WaverlyAddison
If you're asking how a computer sends a text to a phone
The software is connected to a system that has an assigned phone number. When you send a message, the software handles it the same way your phone sends a text using it's assigned number. The recipients phone doesn't know (or care) how the message originated.
With everything being IP, there's not much difference between your smartphone and a "computer".