Posting a dashboard component to a group is a good practice to share and collaborate with team member. While posting to dashboard feed will help us to follow changes of the data in the dashboard.
How to post it? Just hover mouse over a dashboard component, see arrow at top right of the chart component. If you not see it, contact your system admin to enable it. But if you are the admin, see following steps:
1. Enable Feed Tracking for Dashboards
Go to Setup - Customize - Chatter - Feed Tracking
Look for Dashboard object and tick Enable Feed Tracking
2. Enable Post to User or Chatter Group
Go to Setup - Customize - Reports & Dashboards - User Interface
Look for Chatter Options and tick Enable Dashboard Component Snapshots
If you have enable both option above, go back to your dashboard and make sure the page is refresh.
Screenshot below taken when step (2) has not enabled, notice you will see 1 option only.
This screenshot after enable step (2), notice it has option to post snapshot to User or Group feed.
Here is the screenshot post to Dashboard feed and to Chatter Group.
Reference: Posting Snapshots to Chatter