A fund is what is used to designate the area of your organization where a donation will be used. Often, organizations have an Unrestricted fund (where donations can be used to meet any need) and program-specific funds.
A campaign is utilized to track wide-scale fundraising efforts aimed at raising a certain amount of money. The most familiar example of a campaign is a Capital Campaign, in which an organization generally strives to raise a certain amount of money over a defined period of time often to fund a large-scale project, such as a new building. Another common type of campaign is an Annual Campaign.
An appeal is used to track the method with which the donor was solicited to make the gift or donation. Appeals should be as specific as possible-- the title of a direct mail piece, the name/date of an event, the description of a radio ad, etc.
You may add as many funds, campaigns, and appeals as you need in Bloomerang.