Seeing as other answers are either links, or wall of texts, I'll try to keep it short and approachable:

• Encryption, asymmetrical or symmetrical, relies on private keys being private. Once those keys are compromised, the encryption also is (read on).

• By default, in the most simplistic form, it doesn't matter when the content was encrypted, the private key can decrypt it. There are solutions to this problem, making encryption time (or iteration) sensitive.

• For an attacker with enough means, the private keys can always be exfiltrated, and content can be intercepted, but usually there are much simpler solutions for snooping on encrypted content: the devil is in the (implementation) details (this link is an illustration, and by no means an exhaustive list).

• Cryptography is always simpler to go around than to break. So never be satisfied with a cryptography only (or protocol only) audit. There are near infinite of ways to neutralize encryption with a single line of code in a client.

• The architecture is also essential. Client-Server encryption has entirely different use cases than Client-Client encryption (EE2E).

• And finally, Schneier's law:

Any person can invent a security system so clever that she or he can't think of how to break it.

SSL/TLS, the "S" in HTTPS, and other network encryption protocols such as SSH, use a technique called a Diffie-Hellman key exchange. This is a mode of cryptography where each side generates two keys: a public half and a private half. Anything encrypted with the public half is only decryptable by the associated private half (and vice versa).

You and Youtube only ever exchange the public halves of your respective key pairs. If someone snoops on the key exchange all they can do is insert spoofed messages, not decrypt real ones.

Moreover, the keypairs are generated on the fly for each new session rather than reused. This means that even a future compromise of youtube won't unlock old sessions. This is a concept called forward secrecy.

Message spoofing is prevented by digital signatures. These also use the Diffie-Hellman principle of pairs of public/private keys, but use separate longer-term key pairs than those used with encryption. The public half of youtube's signing key, as presented by the server when you connect to it, has to be digitally signed by a well-known public authority whose public signing key was shipped with your web browser.