How Offline Gmail Gets Synchronized?

From Google Groups,

We try to download your most recent conversations along with any conversations that seem to be important (regardless of their age). We also try not to dowload uninteresting conversations. This process is done heuristically and as with any heuristic can and will miss things. We'll continue to tune things up, but more importantly, we'll eventually provide a UI that will allow you to change the settings. Here's a sketch of how these messages are selected:

• Synchronization is based on the date of conversations. The system estimates a period of time to cover (at least 1 week in length) that results in approximately 10,000 messages being downloaded. For an average user, this means Gmail will end up downloading several years of mail.
• Additionally, we'll download any conversation marked with a label that contains less than 200 conversations, has at least one conversation that has been received in the last 30 days and also has at least one conversation that's outside the estimated time period. For many users, this list of labels will include Starred and Drafts.
• Finally, the system determines a list of labels to exclude conversations from being downloaded. For example, Trash and Spam are always in this list, along with any label that contains mostly unread conversations (unread count greater than 99%). So, we won't download a conversation if it contains only labels in this list. A typical Trashed message will not be downloaded, but a Trashed message that contains the label "alpha" will.

At this time, there's no way to customize which of your labels are synced, but we're working on it so stay tuned.