In general, -accia is the feminine form of -accio, both being pejorative suffixes: a giornataccia is a giornata, day, in which nothing goes well, while a donnaccia is a not-to-elegant, not-to-honest donna, “woman” (ok, that would be more like a whore). So, in general, a barcaccia is simply a defective (ugly, damaged, irregularly shaped, whatever) barca, “boat”.
This term, however, came to be used in particular to designate a specific type of mercantile boats, something like a barge (see for instance 1.b of this for a more generic definition, which in any case shows it to be not just a generic bad boat).
Even more in particular, the boat represented in this fountain by Bernini had to have a low hull and to appear partially sunken under the street level, since it commemorated 1598 flooding of part of Rome by Tiber river, but mainly because the Acqua Vergine aqueduct feeding it had too low a pressure to allow a higher structure.