Why was it important to photograph a black hole?

it wasn't a photograph. it was a photo-like rendering created from radio-telescope signals.

No photo has ever been captured. What you no doubt refer to is that colorized radio map of the sky synthesised from several radio receivers. The media loved it. Pop science web sites sensationalised it. The publicity and sale of advertising space ultimately paid for it. Scientific value was likely minimal.

No
It was very important to find one that was facing us dead on so we could look right into it so to speak
It was a first in Astral Photography
 We could see the heat from the friction caused by Matter falling in
Reminded me sort of the Original Star Trek Series which was made back in the Sixties
You know, Kirk, Spock, Scotty etc.
In one episode the went to investigate why Planets were Disapearing
The Culprit was a long conical object that was swallowing everything in its Path
Including Space Ships
An irate Captian from another Star fleet ship beamed aboard the Enterprise, saying he had lost his whole crew to the Object
 In his anger and shame he took out one of the ships shuttles and drove it straight down the Objects throat
Kirk noticed that the light in the Object's mouth had dimmed a lot once it had entered and the Captain was lost
So he beamed aboard the other Captains ship which was a sister ship of the Enterprise and aimed it straight into the Cone
Just before it entered he beamed back and let the ship crash into the Cones throat
Choking it and rendering it harmless to be blown into Smithereens
I used to love that show and what was involved in it was and early idea I suppose of what a Black  Hole could be like

I confess to surreptitiously fishing here to see if empirical evidence still held sway which at least 2 answers suggest it does.(apologies for using you)

Why? 

Because I ask 2 questions in climate change forums re empirical evidence for:

1 co2 warming the planet
2. co2 warming the planet "dangerously" (obama)

Because none exists and the fury the questions invoke made me suspicious science had gone so far down the pan my old physics teacher wouldn't recognise it. His mantra that "science is about experimentation, observations, empirical evidence" doesn't marry with the faith of man made climate doom.

Because it gives NASA publicity. 

Part of the importance was the ability to *see* if what our impressions of a black hole were, in fact, correct. It was basically testing Einsteins views of General Relativity truly held up to what could actually be imaged. 

But - to me - the larger portion was to see *if* it could be done.  It was a project across many nations, with many different types of telescopes, each with different types of abilities.  The amount of data generated and analyzed made sending it via electronic means too slow;  it was easier to simply send copied hard drives to the coordinators of the project.  
Developing techniques like this can help future astronomers see farther, and clearer - which may be a factor when trying to locate planets with life beyond Earth.