Well, the long answer is that it's actually extremely complicated. Not really because the process is particularly difficult, but because the actual software implementations of these things run through so many layers these days. In principle, sending a text message works like this:

Both you and the recipient agree on a code, such that certain binary combination translate to certain letters. For instance, perhaps 00000100 means 'a'. How this code works is ultimately irrelevant, so long as both parties agree. And from there, it's as simple as taking a letter you put in, translate it to binary according to this code, send electrical signals that represent this binary code and then decode it on the other end to get out the letter again. You do that for every letter, and there you go: Text message. Essentially, it's just a fancier version of Morse code.

Now, how this actually works in reality is a lot more complex. In order to understand how sending text works, you need to know how the software you happen to use works. In order to understand that, you need to understand the framework it's built on. To understand that, you need to understand the operating system it runs on. And so on and so forth through understanding web sockets and protocols and the physical connections between servers and blablabla. But, ultimately, the basic idea behind it is as simple as encoding text in binary and decoding it on the other end.

I'm not sure if that really answers your question, as it still strikes me as very vague.