You can customize the appearance of your base by changing its color and icon. On the Airtable free plan, you can choose from one of 10 colors. If your workspace is on a Pro plan, you get access to an additional palette of 10 lighter base colors.
You can change the color and icon of your base from the homepage or from within the base. On the homepage, click the the dropdown arrow for the icon of the base you wish to customize. This will bring up a dialog that you can use to select the color and icon for your base.
If you're looking at your bases in a grid, you can find the dropdown arrow in the bottom right corner of the base icon.
If you're looking at your bases in a list, you can find the dropdown arrow to the right of the base icon when you mouse over that base.
You can also change your base's color and icon from inside the base by clicking the dropdown arrow next to the title of the base.
If you're finding that you want more choices for icons beyond what's available in the icons section, you can also set an emoji as the base icon. Just select the first available icon in the picker (the one that takes the first two characters of the base title), then rename the base by putting an emoji of your choice at the beginning of the base's title. (If you have a Mac, you can bring up an emoji picker by typing CtrlSpace. Alternatively, you can copy and paste your favorite emoji from Emojipedia.)