There is another new feature in Gmail today: Importance Marker.
Seems not all Gmail account can see this new feature today, but if you can see the below marker or popup message in you Gmail, you have the markers.
You can use Importance markers to mark your email as Important or cancel the important marker.
When you mouse hand over the Importance marker, you can see the following tips:
You even can search Importance emails, just like labels emails. see below guide from Google.
Importance markers in Priority Inbox
Priority Inbox displays different colored arrows to indicate different types of messages. A yellow arrow means that a message is important and unread. A gray marker means that the message is important and read or archived. A message Gmail has classified as unimportant has no marker.
If you want to know why a message was classified as important, you can hover your mouse over the importance marker for that message in order to see the main reason why the message was marked important.
If you prefer, you can hide these markers. Just go to the Priority Inbox tab of your Gmail settings and select the No markers option in the Importance markers section.
Gmail treats these markers like labels, so you can search for messages that are important by using the search operator ‘is:important’