The word μορφῇ means "form, outward appearance, [or] shape"1 (occurring in the dative in this context following the preposition ἐν). To be very blunt, translating this as "nature" (as the NIV does) is a poor translation choice. Discussion of God's nature is theologically charged and thus using "nature" in this context could be misleading. The NET translators explain the usage of μορφῇ in Philippians 2:6 by saying:
The Greek term translated form indicates a correspondence with
reality. Thus the meaning of this phrase is that Christ was truly
The next verse uses the same word (but in the accusative) in the phrase μορφὴν δούλου λαβών ("taking [the] form of a slave"). Jesus truly was God, and also he truly was a servant. For an in depth understanding of the usage of μορφῇ both in biblical and extra-biblical writings I have copied a lexical entry for you:
μορφή, ῆς, ἡ (Hom.+) form, outward appearance, shape gener. of bodily form 1 Cl 39:3; ApcPt 4:13 (Job 4:16; ApcEsdr 4:14 p. 28, 16
Tdf.; SJCh 78, 13). Of the shape or form of statues (Jos., Vi. 65;
Iren. 1, 8, 1 [Harv. I 67, 11]) Dg 2:3. Of appearances in visions,
etc., similar to persons (Callisthenes [IV B.C.]: 124 Fgm. 13 p. 644,
32 Jac. [in Athen. 10, 75, 452b] Λιμὸς ἔχων γυναικὸς μορφήν; Diod S 3,
31, 4 ἐν μορφαῖς ἀνθρώπων; TestAbr A 16 p. 97, 11 [Stone p. 42]
ἀρχαγγέλου μορφὴν περικείμενος; Jos., Ant. 5, 213 a messenger fr.
heaven νεανίσκου μορφῇ): of God’s assembly, the church Hv 3, 10, 2; 9;
3, 11, 1; 3, 13, 1; Hs 9, 1, 1; of the angel of repentance ἡ μ. αὐτοῦ
ἠλλοιώθη his appearance had changed m 12, 4, 1. Of Christ (ἐν μ.
ἀνθρώπου TestBenj 10:7; Just., D. 61, 1; Tat. 2, 1; Hippol., Ref. 5,
16, 10. Cp. Did., Gen. 56, 18; of deities ἐν ἀνθρωπίνῃ μορφῇ: Iambl.,
Vi. Pyth. 6, 30; cp. Philo, Abr. 118) μορφὴν δούλου λαβών he took on
the form of a slave=expression of servility Phil 2:7 (w. σχῆμα as
Aristot., Cat. 10a, 11f, PA 640b, 30–36). This is in contrast to
expression of divinity in the preëxistent Christ: ἐν μ. θεοῦ ὑπάρχων
although he was in the form of God (cp. OGI 383, 40f: Antiochus’ body
is the framework for his μ. or essential identity as a descendant of
divinities; sim. human fragility [Phil 2:7] becomes the supporting
framework for Christ’s servility and therefore of his κένωσις [on the
appearance one projects cp. the epitaph EpigrAnat 17, ’91, 156, no. 3,
5–8]; on μορφὴ θεοῦ cp. Orig., C. Cels. 7, 66, 21; Pla., Rep. 2, 380d;
381bc; X., Mem. 4, 3, 13; Diog. L. 1, 10 the Egyptians say μὴ εἰδέναι
τοῦ θεοῦ μορφήν; Philo, Leg. ad Gai. 80; 110; Jos., C. Ap. 2, 190;
Just., A I, 9, 1; PGM 7, 563; 13, 272; 584.—Rtzst., Mysterienrel.3
357f) Phil 2:6. The risen Christ ἐφανερώθη ἐν ἑτέρᾳ μορφῇ appeared in
a different form Mk 16:12 (of the transfiguration of Jesus: ἔδειξεν
ἡμῖν τὴν ἔνδοξον μορφὴν ἑαυτοῦ Orig., C. Cels. 6, 68, 23). For lit. s.
on ἁρπαγμός and κενόω 1b; RMartin, ET 70, ’59, 183f.—DSteenberg, The
Case against the Synonymity of μορφή and εἰκών: JSNT 34, ’88, 77–86;
GStroumsa, HTR 76, ’83, 269–88 (Semitic background).—DELG. Schmidt,
Syn. IV 345–60. M-M. EDNT. TW. Spicq. Sv.3
Concerning the usage of μορφή in both passages, in v. 6 "being" (ὑπάρχων) in the form of God was natural (he was 'in the form of God'), while in v. 7 'taking' (λαβών) the form of a slave was an active choice.
1 William Arndt, Frederick W. Danker and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature, 3rd ed. (Chicago: University of Chicago Press, 2000), 659.
2 Biblical Studies Press, The NET Bible First Edition Notes (Biblical Studies Press, 2006), Php 2:6.
3 Arndt, Danker, and Bauer, 659.