The turbo folder is used to store local copies of files that you access, much like the cache folder (parent folder). However, the files stored here are specific to files that are accessed while Opera uses Turbo Mode to reduce file sizes and bandwidth usage.
Files that are stored in this folder, with the exception of the file dcache4.url, are all stored without a file extension.
The size of this folder varies as new files are cached. The total folder size can be controlled through the Opera Preferences dialog under Advanced -> History -> Disk cache. This is generally set to 20 MB by default.