I am seeing a few people leave private messages on members profiles. It is easy to think you are sending someone a personal message when you are in fact writing a very public message.
Please learn the difference.
A Conversation is private between the members involved. No one else, not even admin staff can see the contents of a conversation unless they are invited into it. Most conversations are just two people chatting privately, however the system is designed so you can invite as many people into the conversation as you like. You don't delete conversations, you just leave them, when everyone has left the conversation it is gone forever.
To start a conversation, look up the member and click on their name or Avatar, you'll see the member card pop up like this.
When you write on someone's profile, this is a public message and can be seen by all members.
Profiles are like forums dedicated to the person, the person is the topic. You can congratulate or commiserate, ask direct questions, offer assistance or ask for it etc. Members have complete control over who can write on their profile and who can see it. To control this you need to look at the 'Privacy' tab on your profile.
Here you can decide who is able to see and post on your profile. Remember all members can see what is posted.