Every time your username is tagged on Twitter with the @ symbol (and assuming you haven’t blocked the user), it works its way to your mentions folder (which is located under the Connect tab on Twitter.com).
Mentions used to be known as ‘replies’ – way back when, this referred to tweets that started with a @username. What’s often confusing for new users is that Twitter handles tweets that start with @username differently than it does those that place the @username somewhere else. It’s a subtle difference, but an important one.
Tweets That Start With @Username
Any tweet that starts with @username on Twitter is interpreted as a reply – that is, Twitter assumes you’re sending this message directly to that person and will place it in their feed (and mentions folder) accordingly.
It’s still a public message (as opposed to a private direct message), and is visible when anyone visits the sender’s profile page. However (and this is the kicker), if you start a message with @username, it won’t appear in the standard home stream of anyone else in your network unless both of you (the sender and the recipient) are being followed.
Tweets That Place @Username Somewhere Else
If a given @username is included in a tweet anywhere else but at the very start, Twitter interprets this differently – as a mention instead of a reply.
What this means is that the tweet will be immediately sent to the home stream of everyone who is following you, and not just the person that was mentioned.
Put literally anything ahead of the @ symbol on a tweet and it isn’t a reply. This is why you see some users placing a full stop before the @username (i.e., .@username), often when they’ve been asked to respond to a given question multiple times by different people, as this allows them to mass-broadcast a “reply” to everybody while also (seemingly) responding directly to the last person who made the enquiry.
A kind of faux reply, if you will. I don’t recommend it. If you want to make an open tweet, then make an open tweet (and tag at the end if necessary). Don’t try and disguise it as something else. It’s confusing enough for newcomers as it is.