I know this will meet with some opposition, but I think Nintendo needs a completely new trajectory. Claiming that they need to "explain the console better" seems to portend that it will be something "hard to understand" again which makes me think its going to focus on some sort of gimmick. At the moment, rumors suggest it will be a portable console with the ability to connect to a home entertainment center and/or comes with detachable controllers. The thing is... this isn't just that innovative (Everyone with an Android phone or any other devices can use wireless display technology), and so we come to the current conceit of my suggestion - its time to stop focusing on consoles entirely!
I personally feel that the idea of the gaming console - as a proprietary platform - has outlived its usefulness and does more to hurt the player base and industry as a whole than help. Decades ago, when general purpose computers cost thousands of dollars and had limited processing power consoles, though expensive for the time, provided a rather affordable way to get into gaming and required purpose built hardware to do so. Today, most modern consoles (ie PS4 / XBOne ) are simply locked down PCs and other devices, using very similar hardware to that provided off the shelf. Focusing more on Nintendo, they have been falling behind for several generations for a number of reasons, but ultimately it comes down to their focus on gimmicks that aren't that innovative or exciting. For instance, the single-touch resistive touch screen WiiU controller pad falls short in an era when multi-touch capacitive smartphones and tablets are widely available. For many gamers, there just isn't much compelling about Nintendo's hardware or ecosystem; the only thing they have is a handful of first party games. I didn't buy a WiiU or a New 3DS, even though I'd love to play Smash Bros, Zelda, Metroid, Fire Emblem, Bayonetta, Xenosaga, and other titles that are on the platform. However, I don't see them as justification to purchase a couple of $200-300+ consoles when I have a PC and mobile - platforms with many advantages! I'd buy all the titles listed above if they were available on PC and/or Android, assuming they were quality ports for reasonable prices, for instance.
Nintendo has fallen behind even the other console manufacturers for a number of reasons too long to assess in an already verbose post. If they have the fortitude to break with the traditional need for control and ownership of an entire platform, I believe they could profit by leveraging their strengths: their games and peripherals. Giving up the costs of running a console platform, mobile or otherwise, will save a considerable amount of money. They could invest it into developing/publishing for the PC and mobile.
It would be easier and cheaper to develop/publish on PCs and the market is growing considerably. Imagine being able to buy the latest Smash Bros on Steam (or Humble etc) and play it against all of your Steam friends remotely, or with others on the same PC. Likewise, sales via Android would be alluring as an alternative to all of the "mobile monetization garbage" out there by charging "3DS style" where a game is $10-40 or so and includes the complete game content (though post-launch development can of course result in expansion style DLC). I'd love to play Fire Emblem Awakening and Fire Emblem Fates on PC and/or my Android phone. Pokemon GO already shows the desire for a Pokemon game on Android (and iOS), with the main criticism against GO being that it isn't enough like a "real" Pokemon game, having an attenuated feature set and mobile monetization style. If they launched the next generation of Pokemon on Android/iOS, I can only see it as a huge success.
Complementing releasing their games on PC and mobile, Nintendo could also develop peripherals for these platforms. Their affection for so-called innovative controllers and other "gimmicks" could be explored as they could create the well-respected peripherals for which they've been known for decades. Furthermore, by developing these peripherals for PC/mobile use and focusing on open driver packages and standards like Bluetooth, they could faciliate offering peripheral / gimmick driven games for those interested as well as provide another entry to the PC controller marketplace with a solid history. This could also provide additional control schemes for gaming especially on mobile, such as a quality bluetooth "dock/controller" that would give gamepad style controls for gaming on mobile devices. Thus, the criticism that 3DS and NX style games would not play well on touchscreen only mobile devices could be mitigated, by offering another control option.
As much as I love many of Nintendo's properties, I can't see myself purchasing any more consoles - not from them, or anyone. I'm tired of platform exclusives, lockdown, and the inability to utilize existing hardware and focus on openness an player experience. If Nintendo can get past their intransigence and move beyond the console paradigm, they could bring their greatest strengths of games and peripherals to targeting the PC, I think they have the potential to break free of their lagging status and change the game entirely, profiting greatly by giving people a better choice.