The following may be a bit more than you were looking for but I thought I'd post it anyways as I thought it a great answer to your question. If you have any specific questions about what any of it means just let me know (or there are others here that can offer a better answer than I). This was recently discussed on B-Hebrew
(a list group for those specializing or interested in Hebrew studies) on March 31, 2010 (IOW it can be checked in the archives on that date for anyone interested...if you wonder why certain comments don't make sense it is because it is part of a discussion among several participants...I hope it is alright with our Moderators that I'm posting this here. FWI...I am not James Spinti, but thought it pertinent to include who wrote the original reply to an identical question to the one posed here.):
But, on the whole concept of 'ap: it is very frequent for the HB to use anthropomorphisms about divine beings, including YHWH.
Here is an excerpt from TWOT (via Accordance--BibleWorks gives the same text):
By the act of breathing, emotions can be expressed. Perhaps it was observed that the nose dilates in anger. God is said to be “אֶרֶךְ־אַפַּיִם“ (lit. “long of anger,” i.e. long before getting angry) in such passages as Ex 34:6; Num 14:18; Ps 86:15; Neh 9:17. The thought is that God takes a long, deep breath as he holds his anger in abeyance, A ruler is said to be persuaded by a display of forbearance, patience, i.e. “the long of breath” (Prov 25:15).
The main use of אַף is to refer to the anger of men and of God. This anger is expressed in the appearance of the nostrils. אַף gives specific emphasis to the emotional aspect of anger and wrath, whereas its synonyms and terms related to them give particular expression to other aspects.
Or, this from Jenni-Westermann (via Accordance):
Much more frequently ʾap indicates “anger,” with an easily understood development of meaning from “nose” to the gesture of “snorting” (in anger), which manifests itself in this body part (cf. Dhorme 80f.; Ug.: WUS no. 345; ? Aram. Cowley, no. 37.8; cf. DISO 21). In almost half the passages that treat human wrath, ʾap is associated with the verb → ḥrh “to become inflamed” (or the subst. ḥᵒrî; primarily in narrative literature: Gen 30:2; 39:19; 44:18; Exod 11:8; Num 22:27; 24:10; Judg 9:30; 14:19; 1 Sam 11:6; 17:28; 20:30, 34; 2 Sam 12:5; Isa 7:4; Psa 124:3; Job 32:2[bis], 3, 5; 2 Chron 25:10[bis]). A holy wrath seizes a person when the Spirit of Yahweh comes over him (Judg 14:19; 1 Sam 11:6). Wrath can turn away (šûb Gen 27:45); this is esp. the merit of discerning patterns of behavior (Prov 29:8).
4. (a) That the gods’ noses (Psa 115:6), indeed even Yahweh’s (Deut 33:10; 2 Sam 22:9, 16 = Psa 18:9, 16; on Ezek 8:17 txt? cf. Zimmerli, Ezek, Herm, 1:222, 244f.; the dual in Exod 15:8) can also be mentioned reflects the OT’s anthropomorphic conceptualization.
(b) Indeed, most instances of ʾap refer to divine anger (168x). All cases of the verb ʾnp qal/hitp. describe divine anger, as does the statement in the Mesha inscription (KAI no. 181.5; DISO 19; ANET 320b): the god Chemosh is angy with his people.
A quick look at the various lexica shows no related words in Hebrew or cognate languages to back up Karl's suggestion of a related root. And, the fact that it occurs in the Mesha stela (Moabite) makes me more than a little suspicious of a separate root.
Hope that helps,
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