I've read on wiki that Monero implemented Electrum's mnemonic seeds.
What are these and what is the differences between other most common seeds?
The seed is a way to encode a bitstring using words that will hopefully be easier to remember.
In this case, the seed is composed of a number of words picked from a 1626 entries list. Each triplet of words can then represent a value between 0 and 4298942375, which is a bit above 2^32. So every 32 bit part of the seed can map to a word triplet, and back to the original value. Instead of remembering a 32 bit number, you remember three words. The monero seed is 25 words: 24 words for the seed (256 bits) and one word as a simple checksum. The name "Electrum" comes from the fact that Monero used Electrum's system.
I can't say anything about the difference with other types of seeds. I'm guessing there's a very large number of variants.
From Moneropedia, a seed is...
A 13 or 25 word phrase used to backup a monero account, available in a number of languages. This 25-word phrase (13 words in the case of MyMonero) has all the information needed to view and spend funds from a Monero account.
In the official wallet, the mnemonic seed comprises 25 words with the last word being used as a checksum. Those words correspond to a 256-bit integer, which is the account's private spend key. The private view key is derived by hashing the private spend key with Keccak-256, producing a second 256-bit integer. The corresponding public keys are then derived from the private keys.
Edit: In other words, a seed is just a private spend key, from which emanate all the other account keys. The mnemonic seed is an alternate representation of it via a list of words, which makes it easy to write it down.