Just like all Apple operating systems, iOS is a derivative of the Mac OS X. Thus, iOS uses Hierarchical File System Plus (HFS+) as its primary filesystem. HFS+ replaces the first developed filesystem, HFS, and is considered an enhanced version of HFS. They are architecturally very similar. The main improvements seen in HFS+ are:
Decrease in disk space usage on large volumes (efficient use of disk space)
International-friendly file names (by the use of UNICODE instead of MacRoman)
Allows future systems to use and extend files/folders' metadata
HFS+ divides the total space on a volume (a file that contains data and structure to access this data) into allocation blocks and uses 32-bit fields to identify them, this means that this allows up to 2^32 blocks on a given volume which simply means that a volume can hold more files.
All HFS+ volumes follow a well-defined structure and each volume contains a volume header, a catalog file, extents overflow file, attributes file, allocation...