South Korea requires all travelers to provide index fingerprints and a facial photo on entry to the country. This applies to all travelers, regardless of visa requirement.
Data collected during the visa process (if required) or on your initial visit to the country will be used at subsequent visits to verify your identity.
As with many countries, South Korea also retains all accessible biometric data on your passport. This data will vary depending on your nationality.
How long will my data be stored?
There is no public policy on how long your data will be stored. It should be assumed South Korea will retain the data indefinitely. South Korea has an unusual relationship with biometric data - all citizens at the age of 18 are required to provide fingerprints to their local police office. Legislation is unclear on if this data is used for criminal investigations or simply identity management, but either way South Korea doesn't state how long information will be stored or what it is used for.
Who is this information shared with?
Currently your data stored with South Korea is not shared with other countries - however, South Korea will likely seek to retain their Visa Waiver status with the United States, this is likely to require South Korea providing access to their biometric immigration databases to DHS in the United States.
What information is required on exit?
On exit the process is similar to entry with one notable difference, if fingerprints have been captured on entry into the country, they are unlikely to request fresh copies on exit.