InMail messages is a premium feature, and it allows you to directly message another LinkedIn member that you're not connected to. If you have a Basic (free) account, then you can only directly message LinkedIn members that you’re connected to. You must upgrade to a Premium account to use InMail messages. You can’t message a member if they’ve chosen not to receive InMail messages in their message preferences settings.
You’re allotted a specific number of InMail message credits based on your subscription type. You can find the number of InMail message credits you have from your My Premium page.