The atomic clocks in the GPS satellites were set with base dates in January 1980 and the indicator for the week was set at a maximum of 1024. This means that on August 22, 1999 the atomic clocks will reset themselves to week 0. GPS receivers, navigation equipment and time-keeping equipment which has not been properly programmed to deal with this change will experience problems when the week counter is reset -- but it is not clear how serious these problems will be.
GPS is based on satellites with extremely accurate atomic clocks and is used for navigation and geographic positioning of objects as well as extremely accurate time keeping. GPS time keeping is used to set the clocks which regulate international communications and computer networks. These GPS clocks are used in banking for money transfers and bank time locks, among other things. They are also used for time keeping in certain scientific experiments.
The bug is expected to be more of a problem with older equipment (pre-1994) than more recent equipment.