My question is simple, what is SegWit, what this actually do? What we can gain with using SegWit? Is there some simple explanation for all this questions?
Bitcoin transactions are like cheques: they need to be signed by the person who owns the bank account that the cheque is made from.
Bitcoin transactions do not accept handwritten signatures, however. They use digital signatures.
So.... the signature for a Bitcoin transaction can be (and are) used for multiple purposes. One purpose is to provide input to the calculation that creates the transaction ID number. This is a number that's used to quickly distinguish one transaction from another by the Bitcoin software.
The Bitcoin txid shares that characteristic with Bitcoin signatures: they can be used for different purposes apart from their basic purpose (serving as a unique identifier for transactions). Or I should say
could be used. There is a problem. A bug.
The bug is that different signatures can be used for the exact same transaction. This is called "signature malleation". All versions of a given transaction are equally valid, miners accept them all.
And so, the problem is this: if one tries to use the txid for some other purpose, there is a risk that an attacker on the Bitcoin network could try to get a different version of your transaction (with an alternative signature) into the blockchain. If you're only sending a regular transaction without anything sophisticated that needs the txid and/or the signature to be what you intended, that's fine, and that's what Bitcoin has been like since the beginning.
But people have devised smart ways to use the txid for something else: Lightning being the obvious example. So......
Segwit takes the blocks and separates (segregates) the transaction data from the signature (witness) data. This prevents all remaining signature malleability attacks (there were other attacks that were fixed in previous soft forks). And that opens the door to all "2nd layer" Bitcoin networks, including Lightning, plus any currently unknown ideas that make use of un-malleable txid or signatures.