Timemachine & Sparsebundle Faq

TimeMachine is Apple's backup solution for all Macs Leopard (10.5) and later

TimeMachine primarily works on your Mac, keeping track of what files change, and scheduling the backups. When it's time to backup again (hourly, by default), TimeMachine looks for the backup location, mounts it, and begins comparing the files that changed against the backup's versions. The changes are transferred (after checking for available space), and TimeMachine cleans up any old backups that have "expired." When the backup is complete, the location is unmounted, and the changes list is emptied.

The backup itself is a sparsebundle (actually a folder) which is a special kind of disk image that can expand (it is "sparse"-ly populated) as necessary. The folder contains a few metadata files and a Bands folder which contains the pieces of the actual disk image.
Inside the sparsebundle is a normal HFS+J disk just like your Mac's, but with a special folder structure. Files are versioned in a way that each dated folder inside Backups.backupdb/<computer> contains links to every file on your Mac, but only one copy of each unique version is stored, saving space.
Starting with Lion (10.7) AFP 3.2 is the only file transfer protocol allowed with TimeMachine. AFP stands for Apple Filing Protocol, and is proprietary to Apple, though an open source implementation called NetATalk exists. Nearly all non-Apple AFP devices use NetATalk.
While Spotlight indexing is used on both your Mac and backup, it does not actually power TimeMachine. Both drives must be indexed for access purposes, like checking for older versions of a file, or running a Spotlight search on the backup to find files by name or content.
FSEvents is the API that actually powers TimeMachine and keeps the backup process quick. Whenever a file changes on your Mac, the kernel logs the change with FSEvents and that log is used to decide which files are backed up using TimeMachine. Whenever the log becomes desynchronized (disk repair, Single User mode access, kernel panic), TimeMachine must perform a complete "depth-traversal" on the backup against your Mac's current state to determine which files have changed. Once the traversal is over, the log is reinstated and a backup follows.

Besides the menu bar item and System Preference pane, there are other utilities that can help with TimeMachine. The tmutil Terminal utility, com.apple.TimeMachine property list, Console (check backupd entries), and freeware app TimeTracker can all help you control and investigate the backup process.

This happens from time to time, and while previous versions of OS X recovered from these issues gracefully, Lion has become more cautious about "runtime corruption" which is almost always a minor issue, fully recoverable without any data loss. It's usually triggered by network loss during a backup, like a power outage, kernel panic, user-forced sleep, or WiFi disconnection, leaving the backup with a "dirty" journal, that is, with files partially written. The journal is meant to prevent such errors, in fact it helps your Mac recover from a kernel panic without corrupting the drive, but Apple has instituted a harsher policy for backups. In such a case, the backup may be marked read-only and locked, preventing access. Check the Applescript at Fix for Read-Only Sparsebundles for an automated fix. Once the bundle is fixed, a backup starts, and verifies the bundle again for safety. Once it finishes, your backup should proceed without further issues.

In this case either or both of your Spotlight indexes have become corrupt and need wiping. This is easily achieved by running "sudo mdutil -Ea" while your backup is mounted. Backups will proceed normally during the reindexing process.