Obsidian doesn’t sync anything unless you use the paid Obsidian Sync service. You can use other sync services on your vault folder, like Dropbox, iCloud, or Git. Regardless of how you sync, Obsidian requires a complete copy of the vault on every device (Obsidian Sync has a setting to exclude folders and file types).
This meta thread has a series of guides for different methods as well as some information about what to do for common problems:
https://forum.obsidian.md/t/meta-post-syncing-between-devices/20983