Connection messages are sent to people who are not your 1st or 2nd connections. Those people are just a cold audience. You can’t text people you don’t know on LinkedIn directly – instead, you have to send a connection request supplied by a connection message before you establish a connection. Once it’s done, you can message them since you’re already connected. There is also a premium option available within LinkedIn paid packages – that is called Inmail: it lets you message people directly who aren’t your connections.