A pullquote block is used to take a brief, attention grabbing quotation from the main text in your post or page and calls attention to it in a graphical way.
Here’s what it looks like when it’s added to the Block Editor.
And here’s an example of a pullquote.
A pullquote is designed to draw attention to a piece of text.
To add a Pullquote block to a page you click on the + icon at the left of any empty block or at the top left of the editor then search for Pullquote, or locate it in the Formatting section, and click on the Pullquote icon.

More detailed instructions for adding blocks can be found here.
Add Pullquote
Once you have added the Pullquote block you add text by typing in the text box and then type the original author in the citation field if your text came from another source.

Pullquote vs Quote
Traditionally quotes were used for quoting text from an external source whereas pullquotes were used for quoting text from your own article. However, the pullquote block includes an option to add the citation for the original author because the pullquote block has more customization options than the quote block.
The appearance of the pullquote block and quote block is controlled by your theme.
Block Toolbar
You reveal the Pullquote block’s toolbar by selecting the pullquote block.
The pullquote block toolbar has options to change block type or style, alignment, bold, italics, hyperlink, inline code, inline image and strikethrough.
The default pullquote style is a simple with borders. You can change the pullquote to a solid color by clicking on the Change block type or style and selecting Solid Color.

This changes the appearance of the pullquote and allows you to set the solid color using color setting options in the block settings. The look of a pullquote block is controlled by your theme.
The change block type can be used to transform to a quote or group block.
The alignment of the pullquote block is changed by clicking on the change alignment icon and selecting the preferred alignment.

Choosing right or left allows you to place another block alongside the pullquote block.
Block Settings
Additional options for the pullquote block are located in the editor sidebar of the block editor. Click on the Settings icon next to the Publish/Update button if you don’t see the editor sidebar.
You reveal the pullquote block’s settings by selecting the pullquote block.

The styles settings allow you to change between the default style and the solid color style.

The main color settings controls the border color or solid color (depending on the pullquote style you are using). The text color is used to change the color of the text.

The editor includes accessibility parameters and displays a warning below the color settings if the color combination you choose make the the text illegible for those with reading impairments.

The advanced tab lets you add a CSS class to your block allowing you to write custom CSS and style the block.