“That region holds a special place in my heart.”
You've just met someone. He comes from an area that you've been to before on vacation. You really loved visiting that area, so you comment on it.
That region holds a special place in my heart.
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A "region" is an area. The size of a region varies. It can be an area the size of a few cities, or the size of several countries. If you're talking about outer space, it can even mean an area that's hundreds of millions of times bigger than the earth.
If something "holds a special place" in your heart, it means that it's very emotionally important to you. For example:
Vikki will always hold a special place in my heart.
That job was horrible... but strangely enough, it still holds a special place in my heart.
You usually use this phrase to talk about things that you don't encounter very often any more, like a friend from your school days, a neighborhood that you don't live in any more, a pet you had when you were a child, etc.