Twitter – know how to make the Tweets private

You need to check "Protect my tweets" on http://twitter.com/settings/account

Only let people whom I approve follow my tweets. If this is checked, your future tweets will not be available publicly. Tweets posted previously may still be publicly visible in some places.

To see all tweets, from anyone, directed to a certain user, you can simply search for "@username". For example, try https://twitter.com/search?q=%40codinghorror to see all replies to Jeff Atwood.

I think I originally misunderstood the question, here's my original response:

Yeah, person A's Twitter replies to person B (tweets that begin with B's @username) are only visible in the Twitter stream of those followers of A who also follow B. I think this feature is fairly non-obvious, especially for new users.

To my knowledge, the easiest way to see also the "@ replies" (without following the other user) is to go to the user's profile (at the Twitter website: http://twitter.com/username, or through some Twitter client) and see their full tweet list there. However, then you'll of course see "@ replies" to everyone, not just to the individual you were interested in. To put it otherwise: no, there isn't an easier way. To see full "conversations" in your feed, you'll have to follow both (or all) parties taking part.