Inode
The structure holding everything about a file except its name — owner, permissions, size, timestamps and where the blocks are.
The name is not in the inode. A directory is in fact a list mapping names to inode numbers, which has two consequences. Several names can point at the same inode — that is what a hard link is. And renaming a file does not touch the file's data at all, only the directory entry.
The inode carries a link count. The file only disappears when the count reaches zero and no process still has it open, which is why space is not freed when you delete a log file a running service is still writing to. The number of inodes is fixed when the filesystem is created, so a disk can fill up with small files while df shows free space — df -i reveals it.