A layout is the body of a report. The "How it looks" after a report is executed with columns in a specific order, subtotals, filters, etc..
There are two types of layouts. 1) User layout and 2) Global layout. Standard settings give all users the ability to create a layout for any transaction that has a layout option. The User layout is only available to that respective user who created it. When a layout is needed by multiple users a global layout can be created.
So how does this tie in with security? Well... when a global layout is to be created from the menu path, the Administration selection will be available (not grayed out) and the Save menu options will provide additional features and options as shown below.
Don't get me wrong, I do think security is important, especially in large, global, SOX constrained, fortune 500 companies. And not to say it's not important in smaller companies, but Security has a much larger footprint when billions of dollars are on the line. However... there are areas that are inadvertently locked down and unavailable in SAP that should be accessible by more experienced users. Case in point is the creation of report layouts. Bottom line, if you find that you are in need of creating a global layout and the above options are not available then you will need to reach out to your security team and request authorization object S_ALV_LAYO to be added to your user profile. Did I tell you how much I love SAP security :)