"Leaving someone on open" on Snapchat refers to the act of opening a message from someone but not responding to it. Snapchat users are able to see when their messages have been opened due to the app's read receipt feature. Thus, if you open a message and do not respond, the sender knows that you've seen their message, but have chosen not to reply. This can sometimes be interpreted as a form of ignoring or dismissing the person's message, depending on the context.