Welcome to Android Forums, Lynn.
If you are using the stock Samsung texting app, texts are sorted by threads. If you begin to type a message and then back out of the app or it times out, the message will be saved to drafts. Any thread that has something saved in draft will show a folder icon next to the contact name. If you open that thread, it will put the draft message in the text entry box so you can finish and send it. Once sent that folder icon disappears and your draft is empty.
I don't know of a way to access the draft folder, or even if there is one. Text messages are stored in a database file.
You always have the options of using an alternate text app from the market, if you prefer it to work differently.