Sharing is caring as a motto between friends:
If friends go by this motto, they share a post or repost something that was funny/enjoyable/interesting, so that their friends can see it too, enjoy it and comment on it or discuss it with eachother. So sharing something with someone means that you care about his/her enjoyment, want some feedback or a conversation about the subject matter or want to inform him/her about something you have learned or seen.
Sharing is caring as a motto between company and customer:
In the context of the OP this motto works too, but is of course a little more specific. What is being shared is information about the company that the customer might want to know (new products, price drops, changes in policy etc.) and the people who are being cared for (by being informed/receiving information) are the customers who follow the company (via platforms like Facebook and Twitter for example). Keeping your customers informed via networking platforms, even if the information is only trivial, can keep your brand or products (seem) relevant, help win over new customers and also keep your regular customers loyal.
I hope that helps a little bit with the meaning of "sharing is caring"?
Remember that the word "care" means a whole bunch of different things: Umsicht, Sorgfalt, Betreuung, Pflege, Zuwendung, Achtsamkeit...
(And there's also a difference between "to care for" and "to care about".)
So you could say that "sharing is caring" in this context is supposed to mean something along the lines of:
"Information teilen bedeutet gute Kundenbetreuung"
"Mitteilen bedeutet den Kunden Zuwendung zu geben"
"Mitteilsamkeit ist Achtsamkeit" ...