It is a list of lists, with the nested list giving you the "name" of the file and the "tmp_name", the location of the temporary file. For instance, to reference the uploaded file from the input tag named "FirstFile" you would use FILES$FirstFile$tmp_name. Here's a code snippet to copy the file to the '/usr/local/uploaded_files' directory:
destination <- file.path('/usr/local/uploaded_files',FILES$FirstFile$name)
NOTE: the temporary files are deleted after the R handler completes handling the request. Thus, it is imperative that you copy/move this file to your desired location before the R handler returns.