How big of a factor is the Alumnii network of a school in regards to getting a job for engineering? I always heard it as important but I don’t really understand the extent to which it matters and how an Alumni connection can get you a job
It’s not the end all to be all, especially for engineering. However, a large Alumni network can help when it comes time to find an internship or your first job. After you’ve been working for a few years, it may not be “as” helpful.
How can an alumni connection get you a job? A lot of jobs are found via networking. For example, you have a friend that graduates a year or two before you and starts working at Corporation X. They tell you Corp X has an opening and then help you get your resume to the hiring manager.
Another example, in LinkedIn, you see a senior manager at Company Y that is an alumni. You asked them if you can connect and ask him/her some questions about Company Y. Being an alumni, they may more likely be open to connecting and answering your questions…networking.
Of course, you can also see a job you like in LinkedIn, apply, be accepted, and never have to deal with networking. 
However, networking is never a bad thing.
I’d say that the campus career/placement center is more important. Of course, often their is linkage with that and alumni network but not necessarily so.
One of the best pieces of advise I ever heard was in 1980s from my high school guidance counselor (who admittedly in general was not much help). He suggested that every college visit should include a stop at the career/placement center … “if it’s a closet with a bare bulb… move on”. Ok, he exaggerated a bit. But it was a good point.
I would say that it’s more important to do really well in college and get to know a professor well. My dad was an engineering professor for about 50 years. Every year, he would recommend students to firms around the state. His recommendations carried a LOT of weight.
It does help a little bit. My D was contacted by an alumnus for a Job opening. That got her through the first round of screening easily. But at the end, the hiring is not decided by that person.