Presence is a feature that allows others to see when you were last seen in Fleep, whether you have read messages (with 'seen-by' indicators) and shows the writing indicator when you're typing.
You can enable and disable Presence features from your account Preferences.
To open your account preferences, click on your profile in the desktop version of Fleep. From the menu that appears, click on Preferences. In the window that appears, you can tick or untick the box for the setting Show my presence status to other users:
Here's a quick demo of the Presence features in Fleep: