Out of context example:

Taking this clever title, "The red pill is pro-rape if you take away the last eleven words from this sentence."
and excerpting it to read: "The red pill is pro-rape ..." ~ TheRedPill
is taking it out of context.

Additional Context example:

Taking this statement: "I love kiwi. I'm a big fan of all fruits, but kiwi is my favorite. It's great in a Sangria!"
and excerpting it to read: "I love kiwi." ~ I
is not out of context.

The key difference is that after reading the additional context, in the first example, the excerpt is not true. The second example adds to our understanding instead of replacing it.

How it matters

Debaters should make either argument as appropriate. If there's additional context you want to discuss to further clarify a topic/position, by all means, raise it.

But calling it "out of context" suggests you're refuting the excerpt. That's not the case for additional context; you're further supporting/explaining it the excerpt.