Appearance is how your blog looks in the mobile apps, dashboard, and search results (not to be confused with your blog theme, which is what your blog page looks like on the web, like at staff.tumblr.com).
Editing your blog's appearance
To edit your blog's appearance, pull up your blog in the mobile app and tap the palette icon at the top of the screen. Tap on things to change or hide them. Adjust your accent color. Go totally nuts.
You can also make these changes using a regular computer, if you prefer. Just click the account icon at the top of the dashboard, choose "Settings," and select your blog from the menu on the right. You’ll see the Edit Appearance button at the top. Click it.
Appearance vs. blog theme
You can check out any blog’s theme (including your own) by clicking on that blog in the dashboard, then clicking the username at the top of the panel that slides out.
Blog appearance is for tailoring how your blog looks on mobile devices, search pages, and the popover that appears when someone hovers over your username. Basically, your blog appearance is for anywhere that is not your blog URL.
Note that your title text, description text, and avatar are universally attached to your blog. If you change them via your appearance options, they’ll change everywhere. And no, there is no way to have different titles, descriptions, or avatars for each location.