The distance of a block from the genesis block on a blockchain which is represented by a number like #4.
The block height is the distance between an active block on a blockchain and the first block on that blockchain (alternatively known as the genesis block). Generally, this distance is represented by a hash and a number which corresponds to the actual number of blocks in-between the one in question and the genesis block. Thus, as the genesis block is designated as block #0, block height is #7 for a block that is 6 blocks after the genesis block. In other words, immediately after the genesis block is a block with block height #1, then #2, then #3, and so on.
A block height functions as a locational description or reference that indicates the number of verified blocks before a particular block.