Obsidian keeps your notes as ordinary Markdown files in an ordinary folder on your own disk. That is the founding decision and everything else follows from it. There is no proprietary format, no account required, and no server between you and your writing. If Obsidian disappeared tomorrow the notes would still open in any text editor, which is a claim almost no other note application can make honestly.
The writing model is built around links. Typing double brackets creates a connection to another note, and creates the note if it does not exist. Every note shows its backlinks, so you discover what refers to a topic without having filed anything. Over time this produces a network rather than a hierarchy, which suits the way research and thinking actually accumulate. The graph view visualises it, and while it is the screenshot everyone shares, the backlinks panel is what gets used daily.
Plugins are where Obsidian becomes strange and powerful. The community has written well over a thousand, and they change what the application is: Dataview turns your notes into a queryable database, Kanban adds boards, Excalidraw adds hand-drawn diagrams, Templater adds scripting, Calendar adds daily notes. A heavily configured vault looks nothing like a default install, which is both the appeal and the trap. Time spent tuning the system is time not spent writing, and the community is quite aware of this failure mode.
Sync is the practical decision. The official paid sync service is end-to-end encrypted and handles conflicts properly. The free alternatives are a shared folder in any cloud drive, or Git for those who want version history, both of which work and both of which occasionally produce conflicted copies. Publish is a separate paid service for turning part of a vault into a website.
Obsidian is free for personal use, including commercial work by an individual; organisational use requires a commercial licence. It is not open source, which surprises people given its positioning, though the file format is plain Markdown so the lock-in risk is close to zero regardless.
Who it suits: writers, researchers, students and developers who want durable notes they control, and anyone who has lost work to a service shutting down. Who should look elsewhere: teams needing real-time collaborative editing, which is not what this is.