Bitcoin is based on cryptography. There is no better place to educate yourself about it than this link: https://www.oreilly.com/library/view/mastering-bitcoin-2nd/9781491954379/ch04.html

There are basically three concepts you must get familiar with:

A bitcoin wallet contains a collection of key pairs, each consisting of a private key and a public key.  Therefore, a wallet can have multiple key pairs.

Private key: The private key is just a number (256 bit long), picked at random. Imagine something like 00101...101

Public key: The public key is calculated from the private key using elliptic curve multiplication (that's pure mathematics). Please make sure to remember that the process of deriving a public key from the private key is a method that is irreversible. I mean, you can't derive a private key from the public key. A private key can be converted into a public key, but a public key cannot be converted back into a private key because the math only works one way.

Address: A bitcoin address is a string of digits and characters that can be shared with anyone who wants to send you money. The bitcoin address is derived from the public key through the use of one-way cryptographic hashing. A bitcoin address is not the same as a public key. Bitcoin addresses are derived from a public key using a one-way function.

Now, since you asked about electrum I will let people answer specifically about electrum. However, what I have written above is NOT application specific. It is essential to bitcoin.