EDIT: From reading the comments below it seems there may be some confusion of the term "Pixel Density". Untill today I have never heard of the term being used in this way. I think I now understand what UKRifter was asking. Perhaps you were referring to the "Oculus Debug Tool" and the variable "Pixels Per Display Pixel Override". UKRifter I believe you are absolutely right. You absolutely can NOT increase the physical number of pixels of your display. I also believe that tool is like you said using a form of anti-aliasing. I think in this case it is using Super-Sampling Anti-Aliasing. The rest of this post is still relevant and worth the read.
Boy oh boy did you ask a tough one. I think I understand the concepts well enough but I may lack the words to explain it. Putting it in terms a 5 year old can understand is going to be tough.
"Hold on to your butts." It may be a rough but informative read.
Pixel Density or PPI is a measurement of how many pixels is in each inch of your screen. Lets use a 1080p 5" Smartphone VS a 1080p 25" PC monitor. They both have the same resolution of 1920x1080 or 2.1 million pixels total. That 2.1mill spread across 25" of screen is going to look good. However if you look close you will be able to see the individual pixels. Now on a 5" screen they have to cram that that same 2.1mill into a much smaller space. Thus a higher pixel density or more pixels in each square inch of space. This forces them to make the pixels much smaller. If you look close you will struggle to even pick out the individual pixels.
Anti-aliasing is a whole other beast. There are also many forms of Anti-aliasing but I will try to simplify the concept. Anti-aliasing does not make pixels smaller or more of them. What it does is hide the edges of pixels that are of contrasting colors. It does this by taking a sample of the two contrasting colors. It then blends the two colors together. Lastly it paints in some of that blended color on the edge of the contrasting colors resulting in a much smother appearance between the contrasting pixels.
Example: (Click to Magnify)
Now what that means in VR is again "A whole other beast". HMD screens seem to range from 5" to 7" but that doesn't really matter. Well it does but it doesn't. Its complicated and I don't fully grasp it but... I will try to explain and simplify the concept. I will use my DIY HMD as an example because I have experience with it. I have a 7" screen with 1280x800 resolution. I am using lenses with a 5x magnification. This gives me a huge perceived virtual screen of about 100°. I am not seeing that 7 inches of screen anymore. I am perceiving the screen to be a huge 100° virtual one. Now if I were to use a 5" screen with the same 1280x800 resolution. I would need to use higher magnification lenses to achieve that same 100° virtual screen. This would result in the pixels being magnified to about the same size. The actual real world size of the screen is somewhat irreverent. It's the perceived virtual size of the screen that really matters. Also the screen type is very important. For example my screen is an IPS-LCD. It has visible black space between its very square shaped pixels. That results in a very visible screen door effect. In contrast the PSVR uses a OLED-RGB screen. It's pixels are still somewhat large but there is very little visible black space between each pixel. That results in a still pixelated image but doesn't exhibit a screen door effect to the same degree.
I hope that was helpful and didn't make you more confused than before. I did struggle a bit to formulate the wording.