OfflineIMAP allows you to read your email while you are not connected to the Internet. This is great when you are traveling and really need an attachment from a message but cannot connect to the Internet.
You can use OfflineIMAP to sync all your email during the night so that it is all instantly available when you wake up. This is a security trade-off -- you gain speed and availability for your email at the expense of having to properly protect the local copy of all the email that is created on your laptop.
OfflineIMAP is designed to contact your IMAP servers and create a local copy of your email in maildir format. You then point your mail client at the local maildir tree and use your mail client as normal. OfflineIMAP can then sync any changes, such as which messages you have read and deleted, back to the server. OfflineIMAP performs a bidirectional sync, so new messages from the server are downloaded to your local maildir while any changes you have made locally are sent to the IMAP server.