In this type of campaign the players agree to play a pre-set series of battles, with each battle affecting the outcome of later battles. Unlike narrative campaigns, which let each battle's outcome drive the story, the links within a ladder campaign are predetermined, so you don't need a referee.
A good example of a ladder campaign was 'The Grudge of Drong', a campaign pack published by Games Workshop some years ago. The campaign consisted of three preliminary battles which led up to an all-out, death or glory final conflict. The first three battles were relatively small actions with up to 1,500 points a side. The final battle involved massed armies of 3,000 points or more. However, the results of the earlier battles restricted what you could include in your army. For example, if the Dwarfs won the first battle (the Battle of Grudge Pass) they could take over a set of mines and have as many war machines in the final battle as they liked; if they lost they could only have a single war machine. The result of the second battle affected the number of runes they could use, and so on.