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NAS means Network Attached Storage. It's basically a very minimal computer without a keyboard or monitor, whose purpose is to house hard drives to provide extra storage space. It can be attached to a home network, which allows you to access its drives from your desktop PC. You can buy special hard drives which are optimized to run 24 hours a day for a NAS, such as the Western Digital Red 4 TB drives I have in mine.

My NAS is a Synology DS416. Here's a link to the Amazon product page: https://www.amazon.com/Synology-DS416-Station-Diskless-Attached/dp/B016EWTC7E/ref=sr_1_1?ie=UTF8&qid=1471576560&sr=8-1&keywords=synology+ds416

I like Synology because it provides an easy to use web admin interface that you can access using your desktop's web browser. It was also one of the brands discussed on the Storj Slack and known to be compatible with Storj. The DS416 is a relatively low end model, but still has enough memory and processing power to run the Storj software. It's a 4 bay NAS, meaning it can hold up to 4 hard drives all linked together. I only use 2 bays right now, but it's nice to have the extra bays available for future expansion.