A lot of it came down to the concept of sovereignty and upset at European laws and legislation being applied to the UK without any apparent say in the matter (which isn't entirely true - lots of misinformation going around).
Part of that feeds into the perception of people of a certain working age that these EU legislations lead to the downfall of the industries that they worked in, particularly with certain types of previously large-scale manufacturing or manual labour industries, like mining, construction and fishing. Normally the perception is that they were all massively in favour of the rest of the EU at their expense, therefore crippled the domestic industries.
Some smaller to mid-size businesses consider at lot of the things being imposed upon them being overly restrictive, burdensome, or expensive on their businesses. This is a particular issue for those who do the entirety of their business within the UK, as many of these legislations were to do with enforcing standards or other matters that are required to prevent one particularly country from exploiting the European Free Trade Area in a fashion that would be unfair to those operating in other countries in the area.
The other argument is that the EU block is too slow at negotiating trade deals as a unit, meaning that, as other global markets are growing exponentially in-size, our ability to negotiate advantageous agreements is being stunted by having to be done in conjunction with the EU block.
Not that I personally agree with many of these points myself - most of those industries suffered from other factors, including increased globalisation outside of Europe and modernisation of process that would have reduced employment in those areas regardless, and much of what the leave campaign brand "Red Tape" are things that stop employers exploiting employees, consumer information and consumer protection, and environmental protections - all things I'm kind of for, really.
There was a lot of deliberate misinformation spread around about the actual process in the EU, not just in the referendum period, but over the last few decades by much of our tabloid press. Whilst there are arguments to be made about how business is handled there, the overwhelming narrative that has been put forth by some parties is that the entire process is dictated in full by five faceless bureaucrats that no-one has any selection and control over, which isn't entirely true in somewhat significant ways.
Also something about European courts overruling our ability to deport people or something.
(I voted Remain, for what it's worth)
-edit- On the immigration front, I should also probably say that some folks thought that it was unfair on non-EU immigration, and that we should be restricting EU movement in order to make unskilled immigration more difficult whilst allowing those in skilled fields an equal chance of easier entry.
