inode (or index node) is a data structure that describes the linux file-system of one object such as a file or a directory.
They are also known as filesystem objects (e.g. files and directories).
Each node stores:
The i-number is a integer that represents the index (ie the location) of the node element in the table storing all nodes (the table is stored as an array)
The common case is one inode for every 2K bytes.
It is possible for a device to run out of inodes. When this happens, new files cannot be created on the device, even though there may be free space available.
ls prints the i-node number in the first column of the report with the i option.