What do we mean when we say it today?
Literally speaking, this phrase means that someone will break into a bunch of little pieces. So basically, whatever has fallen won't be able to be put together again. Someone might dash a plate to pieces, and if that's the case, no amount of super glue is going to make that plate usable.
We've also heard this one used figuratively. People might say someone dashed their heart to pieces. If that's the case, then that person seems rather unlikely to recover.