x bit for directory is also called as search bit. Actually, it enables you to access the inodes of the files listed inside the folder.
So if you want to access /home/user/foo/bar.txt then you must have search access on every ancestor of bar.txt

Quoting from the page

Because directories are not used in the same way as regular files, the
permissions work slightly (but only slightly) differently. An attempt
to list the files in a directory requires read permission for the
directory, but not on the files within. An attempt to add a file to a
directory, delete a file from a directory, or to rename a file, all
require write permission for the directory, but (perhaps surprisingly)
not for the files within. Execute permission doesn't apply to
directories (a directory can't also be a program). But that
permission bit is reused for directories for other purposes.

Execute permission is needed on a directory to be able to cd into it
(that is, to make some directory your current working directory).

Execute is needed on a directory to access the inode information of
the files within. You need this to search a directory to read the
inodes of the files within. For this reason the execute permission on
a directory is often called search permission instead.

Search permission is required in many common situations. Consider the
command cat /home/user/foo. This command clearly requires read
permission for the file foo. But unless you have search permission on
/, /home, and /home/user directories, cat can't locate the inode of
foo and thus can't read it! You need search permission on every
ancestor directory to access the inode of any file (or directory), and
you can't read a file unless you can get to its inode.

Please read more at file permission directory section.

Update: Leo raised a very good question. If we know the inode then can we access a file from a directory having it's x bit unset?
I believe, we should not be able to do so. I did not test it by c program but rather used some handy bash commands to confirm it.

user@user-desktop:~/test$ ls -lart

total 12

drwxr-xr-x 49 user user 4096 2011-11-30 22:37 ..

drwxr-xr-x  3 user user 4096 2011-11-30 22:37 .

drwxr-xr-x  2 user user 4096 2011-11-30 22:38 level1

user@user-desktop:~/test$ ls -lart level1/

total 12

drwxr-xr-x 3 user user 4096 2011-11-30 22:37 ..

drwxr-xr-x 2 user user 4096 2011-11-30 22:38 .

-rw-r--r-- 1 user user    8 2011-11-30 22:38 file1

user@user-desktop:~/test$ stat level1

  File: `level1'

  Size: 4096        Blocks: 8          IO Block: 4096   directory

Device: 808h/2056d  Inode: 95494       Links: 2

Access: (0755/drwxr-xr-x)  Uid: ( 1000/    user)   Gid: ( 1000/    user)

Access: 2011-11-30 22:46:16.576702105 +0530

Modify: 2011-11-30 22:38:12.386701913 +0530

Change: 2011-11-30 22:46:08.876702102 +0530

user@user-desktop:~/test$ stat level1/file1 

  File: `level1/file1'

  Size: 8           Blocks: 8          IO Block: 4096   regular file

Device: 808h/2056d  Inode: 60775       Links: 1

Access: (0644/-rw-r--r--)  Uid: ( 1000/    user)   Gid: ( 1000/    user)

Access: 2011-11-30 22:38:19.846701917 +0530

Modify: 2011-11-30 22:38:16.366701915 +0530

Change: 2011-11-30 22:38:16.366701915 +0530

user@user-desktop:~/test$ chmod -x level1

user@user-desktop:~/test$ stat level1/file1 

stat: cannot stat `level1/file1': Permission denied

user@user-desktop:~/test$ ls -lart level1/

ls: cannot access level1/..: Permission denied

ls: cannot access level1/.: Permission denied

ls: cannot access level1/file1: Permission denied

total 0

-????????? ? ? ? ?                ? file1

d????????? ? ? ? ?                ? ..

d????????? ? ? ? ?                ? .

user@user-desktop:~/test$ cat level1/file1

cat: level1/file1: Permission denied

user@user-desktop:~/test$ find . -inum 95494

./level1

user@user-desktop:~/test$ find . -inum 60775

user@user-desktop:~/test$ find ./level -inum 60775

find: `./level': No such file or directory

user@user-desktop:~/test$ find ./level1 -inum 60775