Gallery display styles are an important and powerful tool to control the way your galleries, thumbnails, and images are displayed to your visitors. It is what allows you to match a gallery's presentation with your own style, but also with the purpose of that gallery (a client gallery isn't necessarily best presented in the same way as a portfolio gallery).
They are assigned upon gallery creation, but can be re-assigned later on. The 4 default gallery styles are a great place to start when setting up your website. And if you want more control, gallery styles offer a great deal of customizability.
You can access your gallery styles via My Website / Gallery Styles. The top menu of every gallery in your administration panel also has an indicator of which gallery style is currently in use. You can click on it to switch and customize your gallery styles.
Customize the gallery styles to change the size and style of thumbnails, pagination settings, how metadata is displayed, and much more. This is also the place to customize the placement of the recently introduced share button. For more detailed information about gallery styles, please have a look at the documentation.
Gallery styles are applied to all galleries using that particular style, so if you only want the changes to apply to one particular gallery, you should create a new style using the "duplicate" button.