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DPI = dots per inch.
Dumbing it down, say your screen is 2 inches wide.
Each icon is 100 dots.
If your DPI is 200, you can fit 2 icons, and they'll be huge
If your DPI is 400, you can fit 4 icons, and they'll be smaller.
It's just using screen real estate more efficiently. Different phones have different DPIs, and as ^ said, with root, you can change it...but I don't want to root this one yet.
Elaborating on the hardware side, it's more commonly referred to as PPI.
Say on a 5" screen, your resolution is 1080x1920 (1080p)
And on a same 5" screen, the resolution on another phone is 1440x2560 (QHD)
Because in the same physical screen size, you have far more pixels, images seem crisper because it's hard to distinguish individual pixels. The downside is that the display needs more power to fire up the increased pixel count, and battery suffers.
General consensus is that 1080p is more than adequate for day-to-day use, because you get better battery life.
If you're into VR, then it does make a difference because the phone is right up against your face and the pixels are more noticeable.
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