What is this electrical device shown in picture?
That's a Hollywood service panel.  In the same way that's a Hollywood starship.  (pretty sure real starships won't look like that.) 

Here's what a real service panel looks like.  By the way, Better Call Saul is set in 2002, six years before Breaking Bad began. 



Unfinished wall area optional; all the wires could be hidden behind studs and drywall and covered right up to the edge of the panel cover,  though that makes the electrical system less maintainable. And by the way, the cables bundled like that is illegal, cables need to cool.

The switch in the upper left is the main; throwing it would do the trick. 



That said, the fiction may be trying to express that there's  some sort of "smart home" equipment going on here, and that might look exactly like that.  That did exist; it just wasn't purchasable at Home Depot and didn't talk to Siri. However, this would only switch the lights; if this scene also cut receptacles and other fixed loads (HVAC?) then only a madman would build a system like that. In 2002 if you shut off power to a PC, you lost all your work.  Smart-home gear had two forks of development: 


Homebrew-tier, with BSR X-10 (powerline signaling) for the hard control, and Apple II / Amiga / Windows 95/98 / Mac OS 9 for logic, scenes, that kind of thing. X-10 goes back to 1977.  (It's really common in the SCADA business to be stuck with heinously obsolete PC hardware because the vendor refuses to rewrite the software for the "platform of the week").  In this branch, the consumer facing controls tend to be pretty hokey-dokey, they are either obviously homebrew, common AC switches retasked for DC, or made-for-X10 deals that fit in a 1-gang space (e.g. standard receptacle cover).   
Industrial-tier, or what they call SCADA (Supervisory Control and Data Acquisition). This is the commercialized version intended for commercial operations large enough to have their own Facilities Departments, e.g. your local community college, a hospital, midsize factory, office building, etc.  That's what it's intended for; nothing prevents the super-rich from installing it in a residence.  Then you get into exotic or bespoke controllers like that one might be.  Again, heinously obsolete hardware is often seen. 




In practical shooting terms, if they had built this set from scratch, they could have had this control actually work the lights.  However, I have to guess they rented/borrowed this facility to shoot in.  In that case, this is most likely a security panel and has nothing to do with the lights.  Right around the corner is a gaffer's best boy, who is throwing the lights off simultaneously. 

Now here's an important fact about film/TV lighting.  The ordinary lights in a location are not nearly enough.  You need to pile on thousands of watts of additional lighting - just shooting a cozy 2-person "between two ferns" shot calls for 2-3 500W halogen fill lights. The problem is light is exponential - double your lumens and you only gain 3db of light.  Office lighting is required by law to be a certain light level...  If you try to shoot in that, you get very grainy shots and your project looks like Blair Witch or Cloverfield. Seriously, installed lighting in a room (or a desk lamp in a "between two ferns" shot) is nothing but a prop.  It doesn't provide enough light to be useful. 

So in that scene, there might be 10,000 watts of additional lighting thrown onto the room behind. The down-lighting is cool, but why is the ceiling so bright between the down lights? Because down lights do not work that way, the ceiling should look almost black in a photo like this because that's how cameras see it. That considerable amount of light is coming from the TV lighting that was added to the room.  

Anyway, one of two things is possible, either the gaffer is throwing the room light switches and added lighting simultaneously (which seems like it would have a chance of causing messed-up takes)... or they have pulled apart the room light switches or supply and tied them into their gaffer board so they throw together. 

It's also possible they even changed the bulbs in the lights, so the characteristics matched - you can't have that copious TV lighting switching off instantly because it's LED, whilst the actual room downlights fade out because they're halogen.  That would look stupid.  

I'm not even starting into matching color temp and CRI, and CRI is more critical because camera eyes aren't human.