Jamieson, Fausset and Brown on Ephesians 5:2

2. And--in proof that you are so.

walk in love--resuming Ep 4:1, "walk worthy of the vocation."

as Christ ... loved us--From the love of the Father he passes to the love of the Son, in whom God most endearingly manifests His love to us.

given himself for us--Greek, "given Himself up (namely, to death, Ga 2:20) for us," that is, in our behalf: not here vicarious substitution, though that is indirectly implied, "in our stead." The offerer, and the offering that He offered, were one and the same (Joh 15:13; Ro 5:8).

offering and a sacrifice--"Offering" expresses generally His presenting Himself to the Father, as the Representative undertaking the cause of the whole of our lost race (Psa 40:6-8), including His life of obedience; though not excluding His offering of His body for us (He 10:10). It is usually an unbloody offering, in the more limited sense. "Sacrifice" refers to His death for us exclusively. Christ is here, in reference to Psa 40:6 (quoted again in He 10:5), represented as the antitype of all the offerings of the law, whether the unbloody or bloody, eucharistical or propitiatory.

for a sweet-smelling savour--Greek, "for an odor of a sweet smell," that is, God is well pleased with the offering on the ground of its sweetness, and so is reconciled to us (Ep 1:6; Mt 3:17; 2Co 5:18, 19; He 10:6-17). The ointment compounded of principal spices, poured upon Aaron's head, answers to the variety of the graces by which He was enabled to "offer Himself a sacrifice for a sweet-smelling savor." Another type, or prophecy by figure, was "the sweet savor" ("savor of rest," Margin) which God smelled in Noah's sacrifice (Ge 8:21). Again, as what Christ is, believers also are (1Jo 4:17), and ministers are: Paul says (2Co 2:17) "we are unto God a sweet savor of Christ."