If you have set up the connections for Facebook, Twitter, etc. through Jetpack but your posts are not being pushed to those platforms try the following.
Make sure you have given permission to editors and authors of your site to use the established Jetpack connections. To do that go back to the Jetpack connection settings.
In the “Publicize posts” section click the drop down arrow to the far right.
Click the check box allowing the social media platform to be used by more than just the administrators. (Obviously this will allow your authors to publish to the specified social media platform so only do this if you trust your authors having this access.)
Once this is done your next published post should also be pushed across your connected social media platforms.
If the post was already published “Updating” the post will not share the post across the social media platforms. You will need to save the post as a “Draft” and “Publish” it again. This should then push the post to the social media platforms.