How to provide import wallet option in Ethereum bloackchain? How does is imports/ how import wallet works?
The Ethereum blockchain contains records of all the ether (eth) currency that has ever been created (as well as new eth created with every new block) and in which all ethereum addresses which have ever contained balances exist in that entire blockchain record (i.e. full validating node).
Regarding, your question of importing an address, I will start by contrasting the difference between importing versus deriving a wallet address, as these are not the same. Conversely, exporting a wallet (creating a backup) is the opposite of importing a backup.
To derive a wallet, you basically "claim" that address using math, as it is derived from a public key which is determined from a starting secret random number which should be generated in a cryptographically-secure manner and which conforms to the secp256k1 curve in terms of the exact size of the random number (cannot be larger than
Therefore, you don't ask for ownership fo a wallet address, it is claimed by you in a permissionless manner during the derivation process (which requires no permission from anyone), based on a secret starting value and the use of elliptic curve cryptography, and related address formatting.
In other words, random secret + fancy math = your ethereum address. And anyone that accesses or guesses your random secret can access your ether (even without knowing the address, as the address is computed from the private key). For more see this related question.
Types of derivation:
The above wallets are derived either one at a time (such as a brain-wallet), or deterministically from a hierarchy structure of extended-public/private keys (such as using BIP32), allowing up to 2 billion addresses to all be connected to one master wallet (crypto vault), and usually can be backed up using BIP39 which provides a recovery phrase that represents a master seed key to the crypto vault (and where multiple cryptocurrencies can be held, using BIP44).
Regarding importing such single wallets or crypto vaults:
Various wallet software, whether online or offline (hot/cold) will usually allow a user to import their existing wallet into the software, which will require entering a private key - for single private-public key pairs, or a mnemonic recovery phrase (12 or 24 words) for crypto vaults.
Example hot wallets would be MetaMask which stores the private keys encrypted in the browser session locally, and another is Blockchain.com which stores the keys on their servers in an encrypted manner that they cannot access, and where both services only allow importing via a 12-word recovery phrase.
Another example, Mycrypto.com is a wallet provider that has a desktop software that accepts the importing of not only private keys and mnemonics but also other forms of wallet backups, such as a keystore file (which is AES-encrypted ciphertext, and common as a wallet backup file format when using Ethereum software such as Geth to export your wallet).
Whereas, hardware devices such as the Ledger Nano or Trezor, can be used as cold-storage allow both the importing of an existing crypto vault, or the generation of a new one.
Wallets are not imported.
ALL the wallets already exists. When "creating" one, you, in fact, ask ownership on a wallet.
I recommand that you read the yellow paper