The factory software image for Edison has SSH access enabled only via the USB Gadget network interface (192.168.2.15). Configuring the board with 'configure_edison --setup' prompts for a root password, configures Wi-Fi, and enables SSH access over Wi-Fi.
I recommend that you leave the root password set if you're joining your Edison to a shared Wi-Fi network. You can avoid entering the root password each time you connect via SSH by setting up public key authentication between the systems you trust and your Edison board.