These sayings are extremely common in the web content and user experience worlds. I find them infuriating, because they sounds impressive but they are fairly opaque and don't really say anything. After all, what kind of context? What does it even mean?
At An Event Apart, they dissected this phrase a little bit.
Image you are planning a conference. You create a website to tell people things they need to know - the twitter hashtag, the address, the registration page, etc. So there's a lot of information here, and you can split it up under tabs or navigation items.
But what if you didn't have to? If you look at the customer journey regarding the conference, there are many phases to attending a conference: the registering, the traveling, arriving and orienting, and then attending sessions. So what if that context - what people were doing at that time - determined what they saw on the website. A schedule of events would be front and center before the conference, but it's much less important afterwards. So the context could be time-based.
By looking at the specific parts of the event, and the time relevance of each, you could shift content based on what priority made most sense during that time.
In addition, you could also alter events based on location. If a person was 50 miles away, geolocation on their phones would give them directions. When they were within the building, it could shift to the wifi password.
The possibilities for events and orientation are limitless.