Every Spotify user has a profile page showing a name, avatar and recent activity. You can also share some of your playlists on this page for other people to see, though which playlists are public and which are private is entirely up to you. Your main Spotify library, where all of your music is collected, is not visible to other people.
Setting Privacy Options
Choose "Edit" and then "Preferences" from inside the Spotify desktop client to make changes to the information you're publicly sharing. You can show or hide your recent activity, your top tracks playlist (automatically generated by Spotify) and the top artists you've been listening to most frequently. You can also set whether new playlists are made public or private by default.
Setting Playlist Visibility
Right-click on a playlist to change its visibility. Tick or untick the "Make Public" option to control whether or not the playlist can be seen by other people. Other areas of your Spotify account, including the Library and Local Files sections, are hidden from other users. The Starred playlist can be made public or private like any standard playlist you've created.