Sometimes you just have to ask.
Tl:Dr - Weekly management meetings were held. Was not a part of them. Asked to be part of them and now am included and have a better understanding of the company's operations.
My company hired me to be an internal IT guy as they would outsource everything (which got to be expensive when people just need their excel worksheet restored they deleted or something easy like getting a printer installed).
Started small by learning the infrastructure, applications and how they do business and the workflow. Now one year later I'm in charge of the security systems, server maintenance, remote help and pretty much I'm acting CIO of this general contracting company. It's not a huge company but I have 4 servers and 100 computers to monitor/update and another 50 in the field to keep updated.
I work directly under the President and CEO and although I'm not a specialist by any means in one aspect I am a good generalist in terms of knowing all the software they use and means of the company only one year later.
Now they would hold weekly "management" meetings to discuss progress on the various jobs. Originally I was never invited to these as they didn't see why the IT guy needed to be involved.
After about a year I asked the CEO, "May I be included in the management meetings going forward so I can better assess the company's direction and help plan for future projects?"
Without hesitation he replied yes and I have been attending them ever sense. Although most of the meetings are about numbers, profit and how the various projects are running it helps to see the 'big picture' and where the company makes most of it's money, where it tends to lose money and my plan is to mitigate that impact with the use of technology and better on boarding in areas where technology can prove useful.
Long story short, ask and usually you will not be turned away from wanting to learn/grow yourself in a company.