What it does
The "manually sync inventory" button will set the Bundle variants as "in stock" when the base variant has stock added to it. It'll also set the variants at 0 stock if the regular variant that they're created from current has 0 inventory.
Why its there
The way the Bundle variant's inventory works is that as long as the base variant has inventory then then the Quantity Break variants will have infinite inventory, simply marked as N/A, and will deduct inventory from the base variant when purchases are made.
When the base variant runs out of inventory the Bundle variants will show as 0. When the base variant gets stock again this button will have to be clicked to set the variants inventory back to infinite. It will also set the app's variants to 0 if the regular version of the variant is already out of stock.
When to use it
This button should be clicked after you change a regular variant's stock level from 0 to a positive number or if it's already at 0 and isn't displaying as sold out. Because app variants need to be created as having an inventory of "N/A" due to a Shopify API limitation, it's a good practice to click this button whenever creating or editing a Bundle group, so the app's variants will have the appropriate inventory level.
Where it is