Your messages are divided into Non Jobs-related and Jobs-related types. All Non Jobs-related messages can be found in your general inbox, the envelope icon right next to your profile picture in the upper right corner. For all Jobs-related messages, you can find them on your Jobs page, in the Opportunities section.
Here's a look at where to find them from the Feed page:
Here's what the general inbox looks like:
Here is a sample of a Non Jobs-related message:
When you want to see Jobs-related messages, here is where you'll look on your Jobs page:
A message (either jobs-related or general) will appear in half-tone, as shown in the above screen capture, if you've already looked at it. New messages will appear normal.