It's just a middle-ground revision like the DSi was.
Both the DSi and New 3DS were released about four years after their respective generation of handhelds began. They were meant to improve the sales of current generation hardware and games, not entirely unlike the PS3 Slim back in 2009. They could be bought by owners of older models who would then either sell their old systems into the wild or give them to family members, improving software sales either way.
Both added some new hardware features (Cameras and storage for the DSi, the second analog, Z buttons, and Ammibo support for the N3DS), and also had increased RAM (quadrupled from the DS to DSi to allow for multitasking and doubled from the 3DS to N3DS), but these were mainly meant to improve performance of current software libraries.
The DSi only ever had four retail exclusives ever released, none of which were notable, while the N3DS has the slightly more notable Xenoblade port but nothing else.
Also, both the DSi and N3DS allow for Nintendo to continue offering handhelds at a certain cost without cheating the customer. Both were launched at the same price the basic model was at for ages, meaning that increasingly cheap hardware would not cut into Nintendo's revenue.
Love and tolerate.
