This passage occurs during Lent in the Revised Common Lectionary (Year A) and Epiphany (Year 1) of the Narrative Lectionary.
This is a text of testing. That verb, πειραζω, appears three times! Testing allows us to discover the nature of something. What do we discover? We discover that the devil is pretty good at tempting...tempting with the flesh, the power and the glory. Even using scripture! More importantly, we learn that Jesus draws his strength from the Word of God. We learn that the Word of God comes from God's mouth, brings life in the wilderness, overcomes evil and is even worshiped by angels.
πειραζω & εκπειραζω ("tempt" or "put to the test," Found in 4:1, πειρασθναι (aorist passive infinitive), 4:3, πειραζων (participle present) and 4.7, εκπειρασεις (2nd person future)): BDAG offers that this word means, "to endeavor to discover the nature or character of something by testing." In this story, we discover the nature of two people, both the devil and Jesus. The devil is the one who tempts us, tempts us with the flesh, glory and finally deceptive power, all so that we would worship him and not God. He will quote Scripture and has no fear of God. We learn also, here, by experience, that Jesus will draw on his power from the Word of God. He alone, and not the devil, is master of Scripture. He will also be ministered by angels, and though human, cannot be defeated by human weakness, but only by the will of God.
Note: Although a slightly different word, εκ-πειραζω, is used when Jesus says to the Devil, "Don't test God," (4:7) I don't think this distinction is key. It means essentially the same thing. Furthermore, because it is a direct quote from the LXX, Jesus (Matthew) is forced to use it instead of simply, "πειραζω." Regardless, this word comes into English in very clear way: "experiment"! (literally e-x-p-e-r-i-m-e-n-t) Jesus is saying, "Don't experiment with God!"
εκπορευομαι ("come out" 4:4, εκπορευομενω (dative participle)) This word here is a fairly common word in Greek -- "come or go out." What is significant here is that is goes hand and hand with the word and the mouth of God. God's Word does not stay still, but goes out from God's mouth. And what does it do? It brings life in the middle of the wilderness and overcomes all evil.
προσκυνεω and λατρευω ("worship" 4:10, προσκεησεις & λατρευσιες (2nd person future)) προσκυνεω comes from the Greek for "forward kiss" as in lean down to touch and kiss the ground in front of the person. λατρευσιες can also mean worship, but has to do with serving God in the temple, or more broadly, serving God as a way to fulfill obligations. The root of the word is payment! In the sense of "paying one's vows" before God. When you put these two together, you have the image of full body worship, with both our knees (on the ground) and our arms (serving God through the offering plate, the acts of worship).
διακονεω ("serve" 4:11, διηκονουν (imperfect)) This word means to "serve" like a waiter serves on tables. It comes into English and the church through a variety of servant ministries. Here we see the other means of worship, not simply on our knees, or with our hands raised, but also on our feet, serving Christ. To connect these last two works, you could argue that the angels fulfill the word of the Lord as the both worship and serve Jesus.
Grammar: εαν vs ει
εαν is nice for translators. It means "if" in a truly hypothetical sense. "εαν" it rains today, the game will be canceled. For example, in Matthew 4:9, the devil says, "εαν" you throw yourself down Jesus, I will give you all of this.
ει, however, is much harder. It can mean "if" or "since" or "because not" depending on the context and the verb moods used around it. Let's look at 4:3:
ει υιος [ει] του θεου, ειπε ινα οι λιθοι ουτοι αρτοι γενωνται
The [ει] has breathing marks that indicate it is a form of the verb "to be," in this case, "are." In fact, most of the words in this sentence an individual learns in the first couple weeks of Greek:
if son are of God, say in order the stones these bread [some form of become]
Because you know the sentence, you probably piece it together:
If you are the son of God, tell these stones to become bread. Why the subjunctive γενωνται? Why ουτοι? For another day! In this sentence, it seems odd that the devil would wonder if Jesus is the son of God. The devil is saying, more likely, "As the son of God, do X, Y and Z." Not only does this make more sense in the narrative, but grammatically, the fact that the verb [ει] is in the indicative and not subjunctive mood, also suggests this.