NuBits is really interesting in how it pegs to the USD, which they explain in the white paper. I'm guessing you don't want to go hunting through there (white papers can be ... daunting), so the short version is....
If the demand for NuBits goes up (ie, lots of people want to buy Nubits, so the price for a NuBit should rise above $1 USD), the custodians of NuShares ("Shareholders") will vote to issue newly minted NuBits to satisfy the demand and therefore drive the price back down to $1 USD.
If the demand for NuBits goes down (ie, nobody wants NuBits, so the price for a NuBit should drop below $1 USD), holders of NuBits are able to "park" their NuBits (aka, keep them off the market) in exchange for dividends paid in PeerCoin, which reduces the supply and drives the price back up to $1 USD.
There's actually lot more going on here than these two things, but these seem to be the main ones. More importantly, they seem to be working as NBT has been transacting around $10,000 USD daily (as of today) and I've only seen the price fluctuate +/- $0.01 USD over the past few months.
If you want the whole story (which includes lots of other mechanisms to stabilize the peg to the USD), take a look at the price stability page on the NuBits website.
The practical conclusion here is: if you ever see NBT selling for more than $1 USD, don't buy it, because the price will be back to $1 USD soon, so you're wasting your money.