Generally when people talk about 'digital printing' it is in
opposition of 'offset printing'. This can be confusing since they
both begin with a digital source.
Offset printing is the kind of printing that newspapers and
magazines use where the print is separated into usually 4 different
color plates (hence the word 'offset') whereas 'digital printing'
relies on a digital file being sent to a RIP (it processes the file
for the printer) then the RIP tells the printer how to squirt the
ink onto the paper. No separations are needed for digital
prints.
The trend in printing is moving away from offset altogether,
however offset's strengths have always been incredible speed (of
printing) and cost effectiveness. As digital printing advances
these differences diminish. HP even has a 'digital offset' printer
that works like a modern digital printer, but with the capacity and
speed to rival an offset printer.