What do these different hotel rates mean?

Your pricing looks like a business traveler oriented hotel in a bigger city. Their prices tend to follow the bell curve during an average week, lowest on Friday & Saturday nights (as business travelers have mostly gone home) increasing towards mid week, then back down to the "weekend" prices. You likely would see opposite pricing schemes at a beach hotel near a big city, as their traffic would be predominantly weekenders.

The price shown for each day is the cost for staying that particular night. A multi-night stay would be the combined costs of each of those nights.

Those are the rates for the days of your stay, not the time that you order. Most hotels have higher prices during times of high-demand, and often higher rates on weekends, etc.

The price only affects the nights you stay. Booking at different dates shouldn't make a difference, unless the hotel hikes up the rates due to demand.

So for your example, book now, tomorrow or next week - if you're staying on the 13th June 2015, you'll be paying their rate of $102.00 USD per night, plus tax of 15%.

Virtually every hotel that is connected via the Global Delivery System has some type of automated occupancy rate tuning algorithm that "tweaks" the rates per room per night. I've seen rooms that typically sell for $500/night as low as $69/night direct from the hotel when they have an unforeseen shortfall of rooms booked.

You might find if you look at this hotel next week, the rates for these dates are wildly different¹. As hotels fill their rooms for any given night, the price is likely to increase. If a hotel receives a lot of cancellations for any given night, the price is likely to fall.

The farther out your check-in and check-out dates are, the more likely the rate is to be stable (unless there is some special event happening in the vicinity of your chosen hotel).

If you deal with a reputable travel agent, and they book you into a room with a flexible cancellation policy, you should be able to cancel and re-book the room at the lower rate in the event the hotel drops the rate as a result of experiencing lower-than-forecast occupancy rates for your given room type and dates-of-stay.

¹ - if you are getting rates via the Internet, you may need to delete any cookies associated with your browsing session to see the lower rates as many sites will only show you rate changes where the rate is higher than it was when you last looked. Another option is to use a different browser/machine later on.

It doesn't matter when you book it, your trip has to be on that date to get that price. For Example: If you stay Thursday, Friday and Saturday, you will be charged (153 + 104 + 102) * 1.15 (TAX) = 412.85.