Initialize means to erase the drive completely. You can try repairing the drive with Disk Utility, but usually when you get this message you will find that the volume is no longer shown in the Disk Utility sidebar. Not a good sign.
See the following:
General File Recovery
If you stop using the drive it's possible to recover deleted files that have not been overwritten by using recovery software such as MAC Data Recovery, Data Rescue II, File Salvage or TechTool Pro. Each of the preceding come on bootable CDs to enable usage without risk of writing more data to the hard drive. Two free alternatives are Disk Drill and TestDisk. Look for them and demos at MacUpdate or CNET Downloads. Recovery software usually provide trial versions that enable you to determine if the software would help before actually paying for it. Beyond this or if the drive has completely failed, then you would need to send the drive to a recovery service which is very expensive.
The longer the hard drive remains in use and data are written to it, the greater the risk your deleted files will be overwritten.
Also visit The XLab FAQs and read the FAQ on Data Recovery.