Since we have New Life by the New Spirit it only makes sense for us to walk in the Spirit. Walking implies that our physical lives are different - that we talk differently, that we do differently.
Jesus is fully man and He is fully God because His Spirit is the Holy Spirit. He was not born with the Sin Nature that the rest of us were. But He had to learn submission to the Father. When He was baptised with the Holy Spirit He was empowered to walk in the Spirit. He went to the wilderness fasting and praying until He was totally conformed to the will of the Father. When He left the wilderness He was prepared to walk in the Spirit.
To walk in the Spirit is to believe and appropriate the promises of the Lord while fellowshipping with Him in the Holy Spirit.