The baptism of Christ signified the Cross, the death, burial, and resurrection that He would soon face to redeem mankind. It signifies the same with us by faith in His finished work.
When Christ asked the 12 if they could be baptized with the same baptism as He, Christ was referring to the suffering of the Cross that all believers will encounter from following Christ. The 12 didn't understand that, but later they fully understood.
"Wherefore, beloved, seeing that ye look for such things, be diligent that ye may be found of him in peace, without spot, and blameless.
And account that the longsuffering of our Lord is salvation; even as our beloved brother Paul also according to the wisdom given unto him hath written unto you;
As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction."
Paul continously spoke of the suffering we must endure, as did Christ, and the longsuffering of the Lord who has extended Grace in order to bring the unredeemed to Himself.
The baptism of Christ was His annointing for His ministry, and proof to the people that He was the One John spoke of. Christ had no sin, He wasn't baptized through repentance of sin. His baptism was His annointing for the suffering to come for mankind.
The water baptism that we partake is our confession of faith in the death, burial, and resurrection of the Saviour. Salvation comes from the heart as Paul said, it cannot be seen, water baptism is a picture of the spiritual baptism (baptism into Christ-- spoken of by Paul) that took place when we believed. Water baptism was essential to the Apostles, it was proof of the unseen, a display of faith in the death, burial, and resurrection of Christ.
Paul said that we have been baptized into His death and the old man is cucified with Him. This is a spiritual baptism, of which, water baptism is a type.