API stands for "Application Program Interface". It is a commonly used method to allow an application program to interface and communicate with another program, computer, sub-process, task, etc, through a standardized and fully documented interface. As it stands now, when eBud or ePoster do a refresh, data collection, post, etc, they are manually requesting pages just like your browser does, in "human readable" form. Then, the "mine" or "farm" the data from those pages because they know the EXACT line and POSITION of each piece of data they want. This is why when eBay makes a page change, eBud stops working until they can realign the lines & positions to the new page.
Using an API, only raw data is passed back and forth. Portions of the API already existing rarely, if ever, change. new fields or changes typically get added to the end of an API in areas "reserved for future use." And API also allows communication to occur quicker since only the raw data is exchanged, not the entire human readable pages (with all the graphics, etc). The API cuts down on bandwidth requirements and server loading since less data is passed.
The problem is eBay designed the API and licenses it to 3rd parties. And, as Tom said, it AIN'T cheap. There are "per month" fixed charges based on the average number of "hits" through the API, plus a "per use" charge for each hit.
Other auction sites such as Yahoo were also developing an API, and I think they were going to license it for free. But Yahoo isn't the 800 pound Gorilla that can charge whatever it likes and get away with it. Yahoo does it to get people to come to the site and cause 3rd party developers to take them seriously.
So, basically this is not something you should worry about for now. I don't think eBay would be foolish enough to demand that all 3rd party "data mining" software use their API, and there is no way they really know you are using eBud anyway. To the server, it looks like you just requested your seller list and auction pages. As I said, it would affect everyone from vendors or management software to counter providers.