First, DNA allows a very high density of information recording. Preliminary estimation shows that a cubic millimeter of DNA can hold one exabyte (1018 bytes) of data.
Second, DNA is the longest-lasting information carrier: it can be preserved for 500 or more years.
A drawback would be that the processes of recording and reading the information are slow and expensive but that might be overcome in the future. DNA is best suited for archival applications, rather than instances where files need to be accessed immediately.
Currently the need for new information carriers is stronger than ever: until 2020, the exponentially growing volume of data stored in computer files is expected to reach 44 trillions of gigabytes. The world is producing data faster than it can be stored. DNA can keep information for hundreds of years and the recording density is thousands times higher than that of SSDs, hard disks or optical disks.