"solo" is slightly misleading and, as with everything in PoE, it's complicated! It's an always online game with large amounts of players, but mostly you only see them in town and the actual gameplay is mostly solo. I say "mostly solo" because you can adventure in small groups, and some people play entirely in fixed duos or groups but for a number of reasons most people play solo.
So your classic RPG (Although action RPG so think Diablo not Skyrim) loop of: town for quests > go off adventuring solo for loot and XP > return to town to sell / ugrade / reconfigure > grow in power > kill series of "dark threats that have come to threaten the land". You rinse and repeat this to the end of the story.
Once the story is done you then have an endgame which is based on randomly generated areas (called maps) using the tilesets from the story and through these you unlock further levels of maps and a bunch of end game bosses. You then play *lots* of maps to gather loot and/or crafting materials in order to become powerful enough to kill these super hard bosses.
The other way to acquire loot is to trade with other players, although that is also more complicated than you would think so many people avoid it entirely and play in a mode called Solo Self Found (ie. no grouping, no trading).
On top of all that, it gets it's longevity for two main reasons:
1) Everything is random and the odds are massively stacked against you. There is a lot of randomised loot but most of it is junk and it takes a long time to acquire high end gear via trading or crafting. If you've played Borderlands it's similar to that but orders of magnitude more punishing.
2) Every three months everything (all characters and loot) is reset and a new league starts with everyone back at level 1 again. Because the economy always resets like this new players can come in and compete because the world is not already full of the in-game equivalents of billionaires. Each league will also add a major new mechanic (the current one is a tower defence style game), a bunch of new loot, updates to various game systems, etc.
Finally, if you are still with me, I would add two more thoughts.
Firstly, I love this game because it came from literally three blokes in a garage in New Zealand deciding to make a game because they loved Diablo II and ending up taking on, and beating, evil corporate gaming overlords Activision Blizzard who just after they started decided to make Diablo III. They were also the first people to replace £60 box prices with a free to play game funded by ethical microtransations (basically fancy armour and weapon effects but no zero gameplay advantage).
Secondly, it's a *hard* game. It's full of arcane systems that are not well explained and the loot system is brutal. It also starts slow and many people quit early on from a combination of the underwhelming start and the obscure, old school way it presents itself. Overall it's a game where the reward comes from overcoming the difficult and adversity of progress rather than dramatic story arcs, fancy reward cinematics, etc. It is a brilliant game, but definitely not for everyone.
https://www.pathofexile.com/game