Why multiple classes of shares?
Here's the general rule when it comes to shares: every shareholder in a class of shares has to be treated the same, but different classes of shares don't have to be treated the same.
Keeping voting control
You could have Class A Voting Common Shares that get to vote in your company matters (such as voting on who the directors should be). You could use these shares for the people who founded your company because you want them to have the highest control (most votes) in your company.
Then, you could have Class B Voting Common Shares. These are for your non-founder shareholders that you want to give some control in the company, but not more than you. So, you give them Class B shares and make sure they have less of them than the Class A shares so they always have less of a vote.
Paying different dividends to different shareholders
Having different classes of shares gives you more options for pulling money out of your corporation, too. Paying your shareholders on their investment is called paying a "dividend". Since different classes of shares can be treated differently, you can pay a higher dividend to one class of shares over another.
For example, you can give your founders Class A shares and pay them a higher dividend since they have put the most money and risk into the company. For other shareholders that you want to pay but not as much as the founders, you could give them Class B shares and pay them a smaller dividend.
Non-voting participation in the company
You could also have Non-voting Common Shares for investors that you want to give shares to but not allow to vote on your company matters. This can be useful for say employees that you want to give shares to as a way of bumping up their pay without giving them control over your company.
What are preferred shares?
Preferred Shares are a kind of share that is a lot like a loan - they have a preferred payback amount. When the corporation is dissolved, the shareholders with Preferred Shares get their investment paid back first out of the remaining assets of the company. Preferred Shares are also sometimes used by accountants for tax reasons. Our default set up is that Preferred Shares do not get a vote for your business legal matters.
A tip, if you're unsure
It's common to include all of these classes of shares in your company in case you need them at some time in the future. There is no obligation to use the classes - they can sit unused until you need them.