You will be seeing PHP code in place of your blog name. The part that is wrong is highlighted in bold above. When you see <a href=" , remove whatever is in between the two quote marks after <em>href and paste /blog/ in its place so it looks like this
Save that and your header link should start pointing to your home page from every page.
You can either use the WordPress Theme Editor, under the Design tab in the Dashboard area, or, if you use an editor, your theme will be in /wp-content/themes, a folder there with the name of your theme