As you may know a stock option is the right to acquire a given amount of stock at a given price. Actually acquiring the stock is referred to as exercising the option. Your company is offering you options over 200,000 shares but not all of those options can be exercised immediately.
Initially you will only be able to acquire 25,000 shares; the other 175,000 have conditions attached, the condition in this case presumably being that you are still employed by the company at the specified time in the future. When the conditions attached to a stock option are satisfied that option is said to have vested - this simply means that the holder of the option can now exercise that option at any time they choose and thereby acquire the relevant shares.
Arguably the primary purpose of most private companies is to make money for their owners (i.e. the shareholders) by selling goods and/or services at a profit. How does that money actually get to the shareholders? There are a few possible ways of which paying a dividend is one. Periodically (potentially annually but possibly more or less frequently or irregularly) the management of a company may look at how it is doing and decide that it can afford to pay so many cents per share as a dividend. Every shareholder would then receive that number of cents multiplied by the number of shares held.
So for example in 4 years or so, after all your stock options have vested and assuming you have exercised them you will own 200,000 shares in your company. If the board declares a dividend of 10 cents per share you would receive $20,000. Depending on where you are and your exact circumstances you may or may not have to pay tax on this.
Those are the basic concepts - as you might expect there are all kinds of variations and complications that can occur, but that's hopefully enough to get you started.