This explanation is gonna be pretty brief. You don't need to know what a tabletop role-playing game (aka TTRPG) is to understand it. In fact, if you just read that and have no idea what it means, don't worry about it, man. Just pretend you didn't see it. Everything will be alright.
The quick version
A solo journaling RPG (RPG = role-playing game) is a game in which the player interprets prompts, and writes things based on those interpretations.
That's like, solo journaling RPGs boiled down to their barest of essentials.
The not-as-quick-but-still-pretty-fast version
In a typical solo journaling RPG, you play as one person and write from their perspective. You might have stats (you might not!) that affect the way you play. Usually, there's cards and/or dice involved. These could be playing cards, or tarot cards, or some other weird shit out there that I don't even know about.
The dice could similarly vary. Perhaps they're all six-sided, but they could be ten-sided, or four-sided (a bold choice), or a mix of different polyhedral wonders.
But you might not necessarily be playing a person. You could be playing an animal, or a monster, or a convenience store (is there a convenience store based solo game? please let me know if you find one).
It's hard to get more specific than this, because lots of SJRPGs (abbreviating from now on—it takes so long to read and type!) are wildly different from each other. Sometimes prompts rely heavily on your interpretation, generation and rolls, sometimes they're pre-written, or appear again and again. The mechanics and how you interact with them can change throughout a game, meaning rolls or cards mean different things based on certain checkpoints.
The best way to get familiar with SJRPGs is simply by reading and playing them. Some are more "journaling" than "gaming", but the discussion of whether "SJRPGs are just glorified creative writing exercises, and ~ aren't real role-playing games ~" isn't one I find particularly interesting.
Just try it out! Have fun! Good night!