My interpretation is that now GW is broken into two sections, the:
- Daily Battles
- Weekly War
Each day there will be a specific Daily Battle against a single opponent. All battles won that day (against that specific opponent, at a max of 5 battles per guild member) are tallied at the end of the day and whichever guild "won" will get bragging rights similar to the current trophy system. This is repeated each day for 6 days. Then, at the end of the week, all the Daily Battles (no matter what day they were done) will be tallied up to give us the winners of the Weekly War. Rewards will then be dolled out based on how a guild did in the Weekly War.
Does that answer your questions? (Again this is my interpretation, as @DonBoba pointed out, Sirrian will be providing additional details later).
Edit: Also, if you miss a day, you can still use your 5 battles to fight the guild you missed at any time during the week, but those battles won't count towards the Daily Battle, just the Weekly War.