Once you've styled a shape, connector, or sticky note exactly how you want it, you can save that style as the default for the board, so every new object of that type picks it up automatically, without you having to restyle it each time.
The Save as default style option will show up for every object type, but what it actually remembers varies a bit:
Shapes: fill, outline, color, and text formatting are all saved
Connectors: line color, style, and arrow endpoints are saved
Text: color, size, and text formatting are all saved
Sticky notes: color and overall text style are saved
Annotations: style and the numbered toggle are saved
Wireframe elements: most components save their full style; a few (dropdowns, inputs, tooltips, and groups) currently only remember size, not color or fill.
Frames: style, orientation, and toolbar options are saved
A couple of things it doesn't cover yet:
Mixed text formatting: if you've bolded or resized just one word within a sticky note, task, connector label, annotation, or similar, that specific formatting isn't picked up, only the object's overall style is.
Size and position, for some objects: for example, a saved annotation default won't carry over its size or position, just its look.
Your saved default only applies to the board you set it on. If you work across several boards, you'll need to set your preferred style on each one individually, there isn't yet a way to apply a default style across your whole workspace.
Save as default style changes what new objects look like going forward, on this board.
Paste style copies a style onto existing objects. Copy an object with the style you want, select the object(s) you want to update, then choose Paste style from the ⋯ menu (or press Cmd/Ctrl + Opt/Alt + V).
Use Save as default style to set your board's look going forward, and Paste style to bring older objects in line with it.