SharePoint Online - Permission Levels

Below is a complete list of the permission levels, what they do and who they are for:

Full Control: By default, this permission level is assigned to the Owners group. 
Contains all available SharePoint permissions. It can't be customized or deleted. 

Design: Create lists and document libraries, edit pages and apply themes, borders, and style sheets on the site.  

Edit: By default, this permission level is assigned to the Members group.
Add, edit, and delete lists; view, add, update, and delete list items and documents. 

Contribute: View, add, update, and delete list items and documents. 

Read: By default, this permission level is assigned to the Visitors group.
View pages and items in existing lists and document libraries and download documents. 

View Only: View pages, items, and documents. Any document that has a server-side file handler can be viewed in the browser but not downloaded. File types that do not have a server-side file handler (cannot be opened in the browser), such as video files, .pdf files, and .png files, can still be downloaded. 

Approve: Edit and approve pages, list items, and documents. By default, the Approvers group has this permission. 

Manage Hierarchy: Create sites and edit pages, list items, and documents. By default, this permission level is assigned to the Hierarchy Managers group. 

Restricted Read: View pages and documents, but not historical versions or user permissions. 

Restricted Interfaces for Translation: Can open lists and folders, and use remote interfaces.

Limited Access:  Enables a user or group to browse to a site page or library to access a specific content item when they do not have permissions to open or edit any other items in the site or library. This level is automatically assigned by SharePoint when you provide access to one specific item. You cannot assign Limited Access permissions directly to a user or group yourself. Instead, when you assign edit or open permissions to the single item, SharePoint automatically assigns Limited Access to other required locations, such as the site or library in which the single item is located. 

Lockdown mode

Limited-access user permission lockdown mode is a site collection feature that you can use to secure published sites. When lockdown mode is turned on, fine-grain permissions for the limited access permission level are reduced. The following table details the default permissions of the limited access permission level and the reduced permissions when the lockdown mode feature is turned on.

Site Settings >> Site Collection features

Permission	Limited access - default	Limited access - lockdown mode
List permissions: View Application Pages	X
Site permissions: Browse User Information	X	X
Site permissions: Use Remote Interfaces	X
Site permissions: Use Client Integration Features	X	X
Site permissions: Open	X	X

Lockdown mode is on by default for all publishing sites, including if a legacy publishing site template was applied to the site collection. Lockdown mode is the recommended configuration if greater security on your sites is a requirement.

If you disable the limited-access user permission lockdown mode site collection feature, users in the "limited access" permissions level (such as Anonymous Users) can gain access to certain areas of your site.