According to the kernel documentation,
/proc/sys/fs/file-max is the maximum, total, global number of file handles the kernel will allocate before choking. This is the kernel's limit, not your current user's. So you can open 590432, provided you're alone on an idle system (single-user mode, no daemons running). File handles (
struct file in the kernel) are different from file descriptors: multiple file descriptors can point to the same file handle, and file handles can also exist without an associated descriptor internally. No system-wide file descriptor limit is set; this can only be mandated per process.
Note that the documentation is out of date: the file has been
/proc/sys/fs/file-max for a long time. Thanks to Martin Jambon for pointing this out.
The difference between soft and hard limits is answered here, on SE. You can raise or lower a soft limit as an ordinary user, provided you don't overstep the hard limit. You can also lower a hard limit (but you can't raise it again for that process). As the superuser, you can raise and lower both hard and soft limits. The dual limit scheme is used to enforce system policies, but also allow ordinary users to set temporary limits for themselves and later change them.
Note that if you try to lower a hard limit below the soft limit (and you're not the superuser), you'll get
EINVAL back (Invalid Argument).
So, in your particular case,
ulimit (which is the same as
ulimit -Sf) says you don't have a soft limit on the size of files written by the shell and its subprocesses. (that's probably a good idea in most cases)
Your other invocation,
ulimit -Hn reports on the
-n limit (maximum number of open file descriptors), not the
-f limit, which is why the soft limit seems higher than the hard limit. If you enter
ulimit -Hf you'll also get