The Swordfish is like an X-Wing, but instead of it consisting of 2x2 cells, it is consisting of 3x3 cells. It is also called a 3x3 Fish.
The X-Wing allows us to eliminate all those 5 candidates.
The Swordfish allows us to do the exact same thing. The only difference is, that this configuration is a bit harder to spot, because it consists of nine instead of four cells.
Why does it work?
We have already shown why this elimination is correct for an X-Wing (by showing all two possible outcomes).
Now assume a cell of the Swordfish to be correct (5).
If you do that, there cannot be any 5s in the same row and column.
What remains of the Swordfish is an X-Wing for which we have already shown that we can eliminate all candidates from the rows/columns.
This is true, regardless of what cell of the Swordfish we assume to be correct.
Another way of showing it
We know for a Row-to-Column-Swordfish that we have to place a candidate in each of the three rows.
So there must be exactly one 5 in the first row of the Swordfish, one 5 in its second row, and exactly one in its third row.
Now if any of the cells were a 5, ...
... we would eliminate one column of the swordfish completely.
Now there is no way of dividing three 5s into two columns without breaking the rules of Sudoku.
This is of course also true for even bigger fish like the Jellyfish.
An incomplete Swordfish is as useful as a complete Swordfish.
It makes no difference if the candidate was ruled out from some of the Swordfish's cells.
This is still a Swordfish, and we can still eliminate the candidate from all of its rows or columns.
In theory, even something as simple as this could be seen as a Swordfish, but, of course, the 5s in the rows are nothing more than Hidden Singles. That is why the sudoku.coach Solver would never find a Swordfish with fewer than two candidates in a row/column.