The lecture will introduce some big concepts, but I also want you to understand how things spread generally. First, hubs are very important in the way information, diseases, fads, memes, etc. spread in social networks. Once something hits a hub, a lot of people (all the hub's neighbors) are exposed. Secondly, weak ties are important. This is because they often bridge groups. Spreading well means that information will cross from one cluster to another. Think, for example, of your first homework where you visualized your Facebook network. To get something to spread among the groups there, it had to hit some nodes with high betweenness and cross some paths that were weak ties to get there.
Also, for the probability lecture in particular, the material is pretty complex. I suggest reading the book which has more detail, and THEN using the lecture to help you through some of the examples there. This week, in addition to the lectures which detail the higher-level technical concepts, the readings will be important. Chapter 10 goes into similar details as the lecture, but Chapter 17 (on Zombies) applies a lot of what we have learned so far to give you some practical ideas (in a very serious context!) of how to think about spreading information (or zombinism) in networks. The Zombies chapter should give you some ideas about how to apply these ideas.