I don't believe any kind of Dreadnought was ever mentioned on screen. It all began with the Franz Joseph technical manual. An image of the ship from that book might have appeared ever so briefly in the background of a TOS movie but nothing audible was ever said.
I'd be interested to know if I'm wrong on that, but I can't recall anything. It is a feature of numerous Trek based games, all the way back to Star Fleet Battles, and on into various video game titles.
--Alex
That's not actually true... there was an audible reference to the Dreadnaught Entente' (as well as several other FJ-based names and numbers) in the comm traffic during ST-TMP.
And there were schematics of dreadnaughts seen on-screen during more than one of the TMP-era flicks.
Now, what is a dreadnaught? Well, most folks just think of that as meaning "a big, bad ship." And, for the most part, that's true, but by that definition, you MIGHT consider the Galaxy class a "dreadnaught," and that's obviously not the case.
A dreadnaught, in classical terms, merely refers to a battleship-type vessel with a specific gun configuration. But in Trek terms, I think that term is obviously primarily obsolete.
In "fanon" work (and I'll consider FJ's stuff to be "fanon" for teh sake of this argument, since GR and his successors, during the TNG-and-later era, did everything within their power to invalidate FJ's stuff), a "dreadnaught" is a large ship which has significantly increased power output and "fleet command" level command-and-control systems.
As a rule, a single dreadnaught is assigned to each major Federation jurisdiction (Starbase, etc) and serves as the primary "vessel on-call" for that post, and also as a "mobile command post" should fleet actions be undertaken. Yes, a "heavy cruiser" like Enterprise would not be the flagship, in those situations... a dreadnaught would.
In the TOS-era, with primary power generation occurring in the engine nacelles, the Federation class dreadnaught had at least 150% of the power output of the Constitution class (and likely also had additional fusion-power capacity as well).
In the TMP-era, the "Federation (uprated)" class dreadnaught had an entire second reactor system of the type the Enterprise class (aka "Constitution (uprated)"?) carried, giving it 200% (plus fusion-based auxiliary power) of the power output of the Enterprise.
Presumably, other TMP-era dreadnaught classes (Ascension, Adamant, etc) would have been comparable in terms of power generation.
The dreadnaughts lack long-range-exploratory features (large labs, etc), have limited cargo capacity when compared to similar-sized classes, have expanded flight decks (embarking both personnel/cargo shuttles and dedicated tactical craft), and have a "fleet command" facility separate from the main bridge.
Typical peacetime roles include "local policing" of the region immediately around a starbase (supporting, when necessary, the smaller craft which are normally dedicated to that function), emergency actions initiated from a starbase (such as rescues of ships in distress), and "shows of the flag."
The typical wartime role is, as mentioned before, "fleet command." It's likely among the fastest and most powerful ships in a fleet, but is not normally going to see a "tip of the spear" role in any combat scenario. Rather, its defenses will be considered largely "robust, aggressive defense." These ships will usually have very balanced firepower, rather than forward-emphasized firepower as is the case with most conventional "ships of the line."
All that is "fanon" information... none of it was ever formally stated on-screen. But, as with so many other things, it was very well-defined and widely accepted prior to the "shutdown of fanon" by PPC legal and the decry of "fanon" by GR in the TNG-and-later era.