What are these orange outlets directly attached to my breaker box?
That recep appears to be right next to your service panel, connected to the panel by a 1" conduit nipple. 

That makes it the "magic electrician's outlet".

It's not required by Code.  It's just a "common practice" for an electrician to fit such an outlet, and place it on a dedicated circuit breaker.  This costs about $10 normally ($5 for the breaker, $1 for the nipple, $1 for the Handy Box, and $3 for a quality recfep and cover). This is generally the first breaker installed in the panel.  The electrician then runs extension cords off it to power tools and lights while wiring the rest of the house.  Alternately, the electrician can power down the whole house (except that one circuit) and do the needed tasks.  

Since it is dog simple, only the two THHN wires to the recep (ground is via the steel conduit itself), it's very easy for the electrician to visually inspect that it cannot possibly be interacting with any other circuit in the house.  So the electrician can be confident that the entire house is powered down. 

I'm not sure why your electrician would use an orange one.  I would look closely at how it is grounded to the ground screw on the receptacle.   Perhaps the electrician wired it intentionally groundless for some reason, in which case I would hope and expect to see it fed from a GFCI breaker.  

Once, a person complained that they were having breaker trips trying to power a gaming PC, laser printer, and (not surprisingly) air conditioner in their home office on a single 15A breaker.  They simply needed another circuit run.  How far is the service panel? "It's actually in this room. Here's a pic." Et voilà, there was the Magic Electrician's Outlet, and on a 20A breaker no less. Problem solved!