I checked out the rare plant database that you were talking about and it doesn't seem like they provide an official API for you to use. However, all is not lost. If you know how HTTP requests work, you can create your own API that talks to the website.
When you enter a String of text in that textbox and hit send to submit a query. It is actually an "HTTP Post Request" that is sent to their web server. Their web server will send you back the list of plants for your query (it will also send you some image files, js files and CSS files for your browser to render it, but you can ignore those).
Of course, all this is happening under the hood, so you probably don't see it. What I did is I used a Firefox addon like "Live HTTP Headers", to view the messages that are being sent. Here is what I found:
POST /data/inv 5|0|8|http://www.rareplants.cnps.org/org.cnps.Result/|E90C92B10BB688CC232EBF994E761ECD|org.cnps.client.InvDataService|readResults|java.util.HashMap/962170901|java.lang.String/2004016611|fulldata|swertia|1|2|3|4|1|5|5|1|6|7|6|8|
The very last line is the POST message. That's what I send to the web server. It contains my query for the plant I'm looking for (in my example "swertia").
The very top line results in me getting an html page called "result.html?fulldata=swertia". My guess is that your plants list is embedded somewhere in that html. (Strictly, just a guess because I haven't spent much time looking into it)
But yeah, so if you wanted something to Google, I'll start out with finding out how you can make HTTP Post requests from the iPhone SDK. Then you can worry about how to receive, extract and display the content after it gets back to your phone.
HTH. Let us know when your project is up on Github. I'll be interested in checking it out. Good luck!