You usually only need the 's' (it stands for secure) in links that involve credentials and user-input (ie: credit cards, SSN, passwords) where sensitive data is involved on websites that have it enabled.
The 's' (usually) signifies that encryption is present. Encryption means your information is translated into a language only certain computers working with that website can understand.
For example, you visit the anti-Fraud ID setup section of the social security website and you input your social security number as 123-45-678, encryption makes it look like 00100101010100110 or it might not even be numbers, it can be random symbols that make no sense to humans because it is in computer language.
You can think of the 's' as in having a private translator named Smith. Smith is helping your transaction with the bank teller. Instead of you talking to the teller in real life, on the internet you are talking to Smith, who then tells the bank teller the information you tell him. Except Smith is speaking in computer language. This means that John, standing behind you in line, can't understand what Smith is saying because it's in a language they don't understand, only the teller and Smith understand it.
Hackers are like Johns. They want to understand what you're saying to Smith, so if they don't understand it, they try to crack the information between the teller and Smith. This is a whole different story (not getting into that tangent). Without Smith, it's very easy for a hacker to get what information you entered in that page, whatever it is.
Now, Smith is part of your browser. He shows up on websites that request him, but he doesn't show up when they don't ask for him.
In the case of sharing youtube videos, you don't need to use 's' (or Smith) because the transaction is public - youtube links never change, and are the same. Youtube links are viewable to everyone in the world, thus the security is unnecessary. However, if you log in to your youtube account and access your profile and personal settings page, you will see Smith is there to help you.
You'll want to have 's' (Smith) if you are every trying to share a website that has some personal information you filled in. Whether your name, address, credit card or something else. Chances are, other people won't be able to see it or understand it anyway with Smith there.
However, any site without 's' (Smith), whatever you share is whatever goes. Sometimes, sharing some sites without the secure protocol lets the other person see exactly what you filled in the box, or it might not. It really depends on how the website works.
