ALTER TABLE engine from MyISAM to InnoDB: why does mysqldump --order-by-primary help me?
MyISAM table is stored as a heap, rows are being placed inside the data file into an empty place they can fit. If you are only inserting then that means appending new rows, but when the rows are being updated or deleted, some gaps are created and then later filled by other rows so the order of full table scan (which is what dump does by default) is not defined in any way.

InnoDB table is organized differently. The rows are stored as items inside a B-Tree "indexed" by the PRIMARY KEY. So entire table is clustered by the PRIMARY index defined. (As a side note InnoDB table always has a PK, if you do not define one, it picks one for you or creates artifical one.) That means that the full table scan is actually executed by scanning all data pages of the PRIMARY index and so the rows are returned ordered by that.

If you dump MyISAM table ordered by PRIMARY, the dump may be a bit slower than the unordered one, but a dump is usually the faster part of migrating so thats mostly a small penalty.

When you insert data into InnoDB table, the B-Tree index dynamically balances itself to keep the logarithmic depth. That often means some page splits are done.

If you insert the data in random order, each row may go to a different part of the tree, hitting different pages on-disk and initiating random splits. That incurs some IO performance penalty and it can lead to suboptimal fill factor (percentage of empty space in each page), as full page is split to two pages only 50% full which means that in bad case your data storage may be 2 times greater than needed (and all queries have to read twice as much data). Another possible outcome is fragmentation of the pages - when logically consecutive pages of the the lowest level of the B-Tree are stored in random separate locations of the disk drive (but this state is not easily identifiable and seems to be a theoretical issue, in practice encountered only rarely if ever).

But if you insert the data ordered by the PRIMARY KEY, the new rows are being "appended" to the table. Only the "last" pages on each level need to be taken care of (and if I understand it correctly - the suboptimal fill factor can be avoided as InnoDB can identify that "appending" is happening and add new pages more effectively). And the pages may be allocated more sequentially too.

So insertion in the PK order leads to faster execution and probably better storage usage in InnoDB tables.