To upload files from the Android app, hit the create button (plus sign), select "Upload Files", and just check the box next to the files you want to upload.
You can also upload multiple photos directly from your photo "Gallery". From the "Gallery" app, just long-press on any photo or even album to select multiple images. Then using the share button, you can upload your photos/album directly to Box.
To Download files, just select the "menu" button from the file/folder you want to download. There are two ways you can download files in Android. You can “Save them for offline use” in which case the file is downloaded and you can access it offline through the Box app. If you need more flexibility, you can also download the file directly to your SD card by selecting "download".