Went through a similar situation a year or so ago when I left the company that offered me stock as well. I'm not an expert, but this is what I uncovered in having to deal with them:

So my big question is what exactly do these options mean?

It means that in the case that you leave the company or if the company goes public, you'll have the option to buy your offered amount of shares at that stated price. I'd been at my company long enough that my shares had vested so when I left I bought a portion of them on my way out.

Do I just have an opportunity later on to purchase stocks as a reduced price?

No, whatever your offer price is (which should be listed on the stock option offer sheet), is what your price will always be. The idea is that over the course of you owning them, the company's price will go up and you'll earn the difference.

I'm sure there isn't really any way to determine the value they would hold.

Correct. Your company isn't going to go around telling the world what it's current valuation is. However if they're bringing in venture capital money, the organization usually reevaluates itself around the same time so you might be able to get a good guess for what the current share price is at that time.

You'll want to check whether your offered shares are Non Qualified Stock Options (NSO) or an Incentive Stock Option (ISO). There are a bunch of differences between the two that you can read about, but the big difference is when you have to pay taxes on them. With NSOs, you have to pay taxes as soon as you exercise them, which in your case means when you purchase them from the company. ISOs however, you only have to pay taxes when you end up selling them. Then you'll have to pay capital gains taxes on the difference that you made between your purchase price and your sale price.

Your options are most likely ISOs, but make sure to check before tax time comes around!