Admin API Access Token allows Big Business to connect to your Shopify Admin with the configuration you set up when you created your custom app for access.
Paste the token you copied from your Shopify Admin. You should have this saved someplace safe because it can only be viewed once in Shopify. When pasted into Big Business it appears with the last four characters displayed, only, to confirm if needed.
If the entry displayed in Big Business does not show the last four characters it it may be an older API Key from a prior iteration of Shopify, which may continue to work.