DVD+RW and DVD-RW are two competing formats of rewritable DVD. Most users probably can't tell the difference between the two, and most DVD players and drives support both formats. However, there are some differences that are worth noting.
DVD-RW was the first rewritable DVD format made available and was developed by the DVD Forum, a group of companies that originally designed the DVD format. DVD+RW was designed by the DVD+RW Alliance years later, mainly as an attempt to create rewritable DVDs without having to pay royalties to the DVD Forum.
DVD+RW and DVD-RW are nearly identical in every way. Video burnt on both discs looks the same, and both can be used for video and data storage. They both cost roughly the same, look the same, and are compatible with most players and drives made today.
DVD-RW was the first rewritable DVD format to be made widely available, beating the DVD+RW format by several years. Because of this, many older DVD drives and players are only compatible with the DVD-RW format and not DVD+RW.
Since the +RW format came after the original -RW format, it could improve upon the original in many ways. A +RW disc doesn't need to finalise, a process that can take several minutes, in order to play. Once the files are burnt to the disc they can be accessed instantly. +RW discs also support "drag and drop" functionality, much like a flash drive.
While older players tend to only be compatible with DVD-RW and not DVD+RW, almost all DVD players and drives made today are compatible with both formats. A drive that supports both formats will usually have a label that says "DVD+/-RW," symbolising its compatibility with both disc types.