Three commentaries I looked at associated the wave offering as a way to show that the ownership of the offering had been transferred to the priests as a gift from God.
For example in Lev. 7:30-35 the emphasis is that these wave offerings were to be a gift to the sons of Aaron.
Lev. 7:30-35 KJV
30 His own hands shall bring the offerings of the LORD made by fire, the fat with the breast, it shall he bring, that the breast may be waved for a wave offering before the LORD. 31 And the priest shall burn the fat upon the altar: but the breast shall be Aaron’s and his sons’. 32 And the right shoulder shall ye give unto the priest for an heave offering of the sacrifices of your peace offerings. 33 He among the sons of Aaron, that offereth the blood of the peace offerings, and the fat, shall have the right shoulder for his part. 34 For the wave breast and the heave shoulder have I taken of the children of Israel from off the sacrifices of their peace offerings, and have given them unto Aaron the priest and unto his sons by a statute for ever from among the children of Israel.
35 This is the portion of the anointing of Aaron, and of the anointing of his sons, out of the offerings of the LORD made by fire, in the day when he presented them to minister unto the LORD in the priest’s office;
This answer focuses not on the significance of the wave so much as it focuses on the purpose of the offering as a whole. Looking at the purpose of the offering as a whole it establishes the Biblical principle that God servants are worthy of an earthly benefit. We see that principle at work in the New Testament when the Bible says that those who have the office of pastor are worthy to receive pay for their work of the ministry.
That is shown in the New Testament in 1 Tim 5:17
1 Tim 5:17-18
17 Let the elders that rule well be counted worthy of double honour, especially they who labour in the word and doctrine. 18 For the scripture saith, Thou shalt not muzzle the ox that treadeth out the corn. And, The labourer is worthy of his reward.
I know some have tried to argue wrongly that double honor means a pastor should be paid twice what other people my be paid. It is their way of being wolves who are fleecing the sheep. The double honor is that they are to be respected and honored one hand and on the other they are to receive double honor by also be paid. He is worthy to receive money from because a pastor is a servant to the people.