Messages can be encrypted at the user level or at the server level. WhatsApp messages are encrypted at the user level, and WeChat messages at the server level. SMS messages are at the un-encrypted level. Encryption is for security. Modern encryptions use algorithms to convert message text into random characters and symbols. It can be decoded only using a key.
Symmetric encryption is one of the oldest methods. Ceaser cipher moves each letter by three. This can be used in combination with a symmetric encryption. Symmetric keys can be decipherable over time. That has led to a concept of public keys. These are asymmetric. Suppose you log in to WhatsApp. It generates a public key and a private key. The public key is visible to all. Private key is the real decoder or has encoding value. A message is sent over a public key lands up in another users system where it is decoded using private key. This is called end-to-end encryption. WhatsApp, Telegram, Signal and other message services use this. It used a mechanism called RSA (Rivest-Shamir-Adleman), along with other systems. iMessage has been doing it what WhatsApp is doing now. Signal has a better standard than WhatsApp. It is the gold standard of messaging services.
WhatsApp generates metadata, and though messages calls, bites, photos and videos are encrypted, but not the metadata, and can show who you are talking to.
Telegram offers end-to-end encryption once the service is activated. And such convesations are in secret chat where messages are deleted after a specific time. Telegram, however, leaks more metadata than WhatsApp does.
Signal too has an additional feature called disappearing messages. It deleted within a few minutes or hours or days whatever is on server.
People keep back up of their chats on Google. This means that chats can be decipherable on Google server. Disappearing messages ensure that nothing gets saved on any of the servers.
Despite this, the messaging apps are not completely safe. With malware, nothing is safe. Someone can mask your private key and your public id.