Content types and columns use Groups to organize them. These are used so things are easier to find as there are a lot of default columns and content types (600+ columns and 80+ content types). As you turn on more features you will continue to get other content types and columns added to your site for you to use. You can access the site column and site content type through the Site Settings page.
Once you go into either page you will see the information organized by Groups with a Show Groups drop down on the top right of the page to easily filter.
What you WON’T see on either of these pages are a collection hidden content types and columns. A good example is the overall Title column for the Item content type. This is a very crucial column that is used across many site content types. So if you change the Title column at the site level, it will cascade to all of your content types and lists that are using that column. I have worked with many clients that did not fully understand what they were updating when they did this so it’s fairly common to see a field like this renamed. If you go into the site columns page you will not see this column because it is part of the _Hidden group. If I go in through site content types -> Item -> Title column, you will see that the column exists in the _Hidden group.
To change the group of this column you can either select an existing group or create a new group.
Once you make your changes the column or content type that you changed will now be viewable under the site columns or site content types page in the group that you selected.
Now what if you wanted to change this back or add a new column or content type to the _Hidden group? When you go back to the edit page you will see that under the Existing group drop down you don’t have the _Hidden option.
All you need to do is type “_Hidden” in the New group text box and it will move it into the _Hidden group and it will NOT create a new group.
Now when you go back to the site columns or site content types page you will no longer see what you moved to the _Hidden group.