I don't understand what it is you don't understand. "There is" means "there exists"; it is a very common construction, and its use here is no different from any other use that I can see, It is a way of introducing something.
The caption was not written by a native English speaker. There are two errors and one dubious phrase.
1. "There's is" would literally mean "There is is". Clearly wrong.
2. "you need to get you out of bed" is incorrect. You can either say, "You need to get out of bed", or you can use the reflexive and say, "You need to get yourself out of bed".
3. "to stop its ringing". This is grammatically correct but not idiomatic. The phrase uses the gerund form of "to ring". It uses it correctly. However a native speaker would probably use the present participle. Either we could say, "to stop it from ringing" or "to stop it ringing".