ok, well I really recommend you do lots readings other than the CSU stuff to get a better grasp. My attempt to explain it to you probably won't be that great, so bear that in mind haha.
In essence, the concept of a globalising world is where physical boundaries between the global and local areas in the world are become more and more blurred, due to advances in communications and evolving economic, social and political ideologies. This disintegration of these physical boundaries means the global community is able to become more integrated - essentially what they call a "global village", where the exchange of ideas, trends, etc. happen at unprecedented rates.
With the local stuff, there's like two things you want to look at in a globalising world:
- the homogenisation of the world (i.e. society is becoming more integrated and less individualised and we are essentially more similar)
- the heterogenisation of the local communities (i.e. local communities are resisting the impacts of a globalising world and are aiming to become more distinctive and "localised")
there's a lot of other stuff that goes with it, I've given you a super basic summary but it should be enough of a starting point for you to get into the topic
I hope this helps!