I believe the first I heard about ho'oponopono circa 2003 is one of those "if it comes in threes, pay attention" serendipities. I'd already been doing my own process of watching and reclaiming my projections and shadow for several years before (also before I heard of Byron Katie).
I heard about it in different circumstances from different sources all within a few days. Anyhow, Dr. Len (via a blog post by Joe Vitale) was the one of those three ways (I am pretty sure the other was A Course in Miracles instructor).
Recently, Joe Vitale release a few clips of Dr. Len in a Ho'oponopono workshop video. I'll share some transcripts of those, but you can also watch the three parts for yourself at www.zerolimitsonline.com.
Below is an transcribed piece starting at 17:30 spoken by Joe Vitale describing how he uses the process (ha, or more accurately, how it uses us):
"When I start thinking that there is somebody or something that is troubling me out there, and your first response--isn't it, from a data perspective-- is to change them. Which is a little bit like I wake up and I'm unshaven and I look at the mirror, and go, "Man, I need to shave" and I start shaving the mirror. It doesn't work that way. I got to shave HERE, and when I shave here the mirror starts to look a lot better...So the thing we're cleaning on isn't anybody out there or anything thing out there-- what you're clearing on is that ball of perception, energy, feeling that you have when you think of out there--that's the thing. When he was working with the mental hospital he was not seeing people professionally one-on-one. . . as he would look at their files he would feel what he's feeling...--it could be rage, it could be shame, it could be embarrassment, it could anger--whatever he's feeling, that's what needs clearing. He's feeling it in him as it is being triggered by what it feels like being triggered by what he perceives to be a person outside.... in this case, he's looking at paperwork, and it's triggering the buttons.... He's feeling it in here, and he's taking it to what I call the Divine." - Joe Vitale
Basically how I interpret this is that if something is bugging me out there in my external world (typically I clear on the immediate sphere), or seems off kilter like dis-ease (some things are unbalanced or out of harmony in the world-at-large although that is hard to truly judge until we clear a lot of subconscious programming), it's time to clear that programming that we share.
And basically this expresses a viewpoint that the external world is more like a 3D hologram that the brain's visual cortex interprets as a fundamental reality, although it is decoded, or interpreted from a level of reality that's more about frequency, vibration patterns, etc. (visual cortex for eyes, but the other senses are also deciphering reality from the fuzzy set of waves and particles). And the subconscious can and may store up and hoard all sort of ready-made interpretations (i.e. memories) and overlays that can distort the perception of the pristine vibrational level occurring dynamically. And throw in the idea of "collective" unconscious, and you're getting hotter.
“If the doors of perception were cleansed, everything would appear as it is - infinite." - William Blake
I'm doing a lousy job of explaining this. Go read The Holographic Universe, by Michael Talbott, for starters. Or you can just go for the direct experience and see that there's no other, there's no out there--one reality, as Deepak Chopra calls it.