This page allows you to customize your blog theme. Turn on/off options, or add texts to your blog theme, and edit your theme HTML. Notice that your customize page is a separate page from your Tumblr account setting. You can't change your profile from your customize page, but there's an avatar upload feature on your customize page too!
I am on mobile, can I access this page?
You can, but we recommend that you customize your theme on your desktop. Tumblr's mobile app doesn't have an in-app customize page. You have to use your mobile web browser to customize.
So, how do I access this page?
Method 1: From your blog.
Go to your blog dashboard. Alt + Click on your avatar, or blog name under your username on your dashboard. This will take you directly to your blog page. You can enter your URL on your address bar too if you know your full blog URL.
Click the palette icon on your blog.
Method 2: Your account setting.
Click this Tumblr blog setting link. This is the direct link to your blog setting. If you are not logged in, you have to login first. When you are redirected, click 'Edit theme' button. Notice that you have a separate customize page for each sub blog you may have. If you would like to access your sub blog's customize page, click your blog in the 'Blogs' tab as in the screenshot.