If you have an appropriate Android device Google Now will (apparently) display information based on your current context (e.g. if your phone learns where work and home are it might display information about traffic jams on the route home around the time it believes you will be traveling). You need a logged in Google account to use this feature.
OK Google is a way of using your voice to interact with your device (or Chrome web browser). So if I have the appropriate phone and it's been set to listen I can say "OK Google" and it will activate an app/mode where it will accept further voice input. On the Android phone I saw (and in my Chrome web browser on OS X) I can then ask it "What's the weather like?" and it pops up some weather related information and speaks back "It's ten degrees in ". Sometimes when you ask it questions just does a web search other times (on the device) it would start applications (e.g. mail) and so on. You do not need to be logged into Google to use this feature.