For those that understand Mr. Robot

The item(s) listed as #1 is your "best current option" given the other gear you're currently wearing.  

The "best in slot" piece will be your #1 option, once you've collected most/all the other best-in-slot pieces as well (best-in-slot is calculated as a full-set of gear, not single pieces, even though sometimes an individual part is so wildly above its competition that it becomes a no-brainer, e.g. legendary weapons).   

At least, that's how it (seemed to?) work for Retribution when the site was first opened to the public.

Keep in mind that, according to Blizz, badge gear should NEVER be your BiS item. It is intended to be kind of a "fill-in" piece between tier pieces. Some casual players will never see H Rag and therefor, for the time being at least, VP gear will be thier only choice for an upgrade. That said, the new LFR will help players immenely til the new expansion comes out.

Mr. Robot takes into account all your stats, current gear and other variables to create their list of BiS items for you. As you change so will the priority list of BiS items that it creates for you. The #1 BiS item will be what you want under ideal circumstances, the #2, #3 and whatnot thats listed as BiS for you is exactly that, BiS for you at this particular time of your gear set, stats and whatever else they use to calculate with.

My hunter has an item level of 373. Mr. Robot still says Tia's Grace (IL346) is my BiS trinket. Thats because taking into account procs, spec, stats and other gear bonuses, it probably gives me a few K xtra dps. My judgement says to go with something with a higher IL and a similar proc and then test it out over a few scenarios to make sure it helps and doesnt take away from my dps. As an SV hunter I survive the dps charts by doin massive AoE damage, Tia's Grace may be the reason for that, or it may not, but why fix whats not broken.

Use Mr. Robot as a guide, but it's not carved in stone, test things out and see what works best for you.

In addition to what other have said, Mr. Robot weighs items 'individually' in that list, so an item with a high priority stat like Hit or Expertise (Dodge, Parry for tanks...)  will move an item up that list.  BUT, once you reach a hit cap, expertise cap, or start with dimishing retuturns on a stat (haste cap) an item furthur down the list may provide more returns 'as a part of your overall gear set'.  

Also, Blizzard does interesting things for stat weighting: e.g. Porcelain Crab (iLVL 346) from Throne of the Tides was BiS through Tier 12 content (iLVL 378) for Blood DK's.  It still sits above a significant portion of new LFR gear and gear from the new heroics, so iLVL isn't the be all end all when looking at lewts.

Also you may give up your current BiS so that you can get a set bonus.  I usually look at the points diff in teh rating if its only like 200 then it really doesnt matter.  It's also more complex for heals casue you may not really need that spirit and they rank spirit as a priority.  It's a great guide I really like ti but you have to know your toon also and simple math doesnt always do it.  Another example would be trinkets they are very hard to determine.

Oh, I don't use it as the be all end all by anymeans. Often times I'll look at it and think 'Ya, I know you want me to do that, but no.' It's mostly useful to remind me what needs gemming and enchants, and I look at the item lists out of curiosity. I'm just confused when I'm looking at the upgrade list and the #2 or #3 item says BiS at the top.

For example, if I load up Cile and look at neck pieces it says BiS Fireform Choker (heroic), then gives me #1 Opal of the Secret Order, and #2 Fireform Choker (heroic). So that means with my current gear/spec Fireform Choker would be the best piece for me, but with ideal gear I'd want Opal of the Secret Order? Because the Opal is VP, if it will be my ideal down the road why not get it now, and not stress about wanting something from hardmode Staghelm?