How does browser verify if SSL certificate is issued by trusted CA? Do browser verify this by ask CA's server? Or it's just the case that only CA can issue those certificate.
You want to read about the topic digital signature. A digital signature allows someone (the CA) to claim that they have authored a data (a certificate containing claims), in a way that are impossible to forge.
Understanding digital signature starts with Public key cryptography. The CA creates a pair of keys: private and public key, that are mathematically linked such that using their private key and a hash of the data, the CA can compute a number (the digital signature) that can be verified by other people that had the linked public key.
Browsers ships with the public keys of a number of trusted Certificate Authority, which it uses as the root of trust. Using this repository of public keys, the browser doesn't need to contact the CA to validate the signature (though note, it does need to contact the CA to verify that the signature hadn't been revoked).