As of Android 3.1, Google has added support for reading USB drives to the Android platform. This means that you can plug in a USB drive and access its files directly from your Android device. There is no need to root your device or install any third-party apps; all you need is a compatible Android device and a USB drive.
To access your USB drive on an Android 3.1+ device, simply plug it in to the micro-USB port on your device. Your phone will automatically detect the drive and prompt you to open it in one of three ways: via the stock Android file manager, through a third-party file manager app, or using the MTP option (which allows you to transfer files between your computer and your phone).
Once you've opened your USB drive in one of these ways, you can browse its contents and copy/paste/delete files as needed. Keep in mind that not all Androi devices are able to read all types of USB drives; if your drive is not recognized, it may be formatted incorrectly or use a unsupported file system.