In the context of

Doesn't it mean, 'in terms of' or 'as far as ... goes'?
Can you use it in the following context: 'In the context of Steve's story, the police said,...'

It has a very subtle connotation. You would use something like "in the context of" when you want to emphasize that a given statement or fact has a significantly different meaning if used in a different context. I wouldn't use it in your example. That exact wording is rather atypical, actually, so let me just give you an example where emphasizing a different context is used.

A:"I punched Larry in the mouth yesterday."
B:"Dude, you're awful. You're always punching people lately."
A:"You weren't there. If you saw it in context, you'd understand. He had it coming."

So in this example, 'A' punched a guy, but because it was in a specific context--maybe Larry was being a bit of a jerk--it's not as bad as 'B' initially thought.

I can't think of one where I would use "In the context of" specifically. Maybe someone else can come up with one.

The context is the immediate environment of an event -- what was going on, who was there, what led to the event, why things turned out the way they did. So when someone says something has to be understood "in the context" of its occurrence, that means that there is more information that you need to know to fully understand the situation and the implications -- all that information won't be fully conveyed in the words or the deed in question. So if the words or action are "taken out of context", they might well be misunderstood or misinterpreted by someone who didn't see the wider picture, or didn't have access to the full story.

Some examples:

"In the context of gender identity issues, the word 'freak' is very offensive."

"In the context of race relations, references to primates, such as 'ape' or 'monkey', should be avoided."