Probably won't hurt anything to format it.
If your new flash drive is a large one (maybe 64GB), then it could be formatted NTFS, which your Mac can't write to natively.
Open your Disk Utility (in your Applications/Utilities folder.
Insert your new flash drive.
Select the drive (might show a line with the model/name Ryval, so select that line)
Click the Partition tab, then click the drop down for Partition Layout, and choose 1 Partition.
Click the Options button, and change the selection to GUID Partition table, and Click OK
Click the Apply button, which will ask if you really want to erase the drive, which is OK.
The re-partition will take a few seconds, and you will be able to use the drive on your Mac.