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"This" as the start of a reply is shorthand for "the comment I'm replying to makes a very good point that I agree with entirely" (and usually "and here's my take on what (s)he wrote"), rather than "what you are about to read is the answer you are looking for".

"This." is shorthand for "This is how:"

It is a +1 mechanism for places that don't have voting, so far as I can tell. I have seen it quite often over on reddit. It used to be rather frowned upon here but the removal of visible vote numbers is likely to encourage it.

Basically what stonemetal said. With no vote count, it's a visual indication that I'm in agreement with what the person I'm replying to has said, and extending upon it.