When you select one of these buttons it will open up a new column/group to the far right. You may rearrange the columns later by using the arrows at the bottom of each column. SEE THE BOTTOM OF THE PAGE FOR NOTES ABOUT REMOVING COLUMNS AS THIS CAN BE TRICKY.
Please note that if you every click the "X" in the uppper right hand corner of a column you will get the following dialog box. I recommend getting a Tweetdeck account so all of your columns, groups, and searches cam be restored if you accidentlally delete them. Just don't check the Permanently Delete box.