When you edit a document offline, your changes are stored locally on your device. When you go back online, your changes will automatically be synchronized into the document.
Quip is designed so that your offline changes are merged in exactly the right place, even if someone was editing online at the same time. This also works if multiple people are editing the same document offline. If two people edit the same section offline, both sets of changes will appear when the people come online. Edits will appear sequentially based on the order the changes were made offline.