This has been a hard verse for many because of a few issues: 1) Where does it fit in relation to the preceding and the following verses; and 2) What does it mean to pray lifting holy hands?; and 3) What about the women, are men only to do the praying?
It seems clear from the conjunction oun ("therefore") that this verse is referring back to the previous verses. In other words, in most translations, the paragraph break comes after verse seven and then verse eight begins the new section continuing until 2:15. However this should not be the case. With the oun ("therefore"), it is referring to what has just been spoken. In essence, Paul has just stated the need to pray for governmental officials and how it is God who desires all men to be saved (including those in political leadership). Furthermore, Jesus Christ is the only Redeemer for the sins of all mankind. It was for this reason that Paul is an apostle and a preacher, namely, to get the Gospel of the Lord Jesus Christ out to a godless world. Thus verse eight forms a great inclusio (v.1 beginning with prayer and now v. 8 ending with prayer and everything from vv.2-7 is enclosed between this theme of praying). In sum, this verse goes with the preceding section. The beginning word "likewise" (hosautos) in v.9 shows that this is the new section/paragraph.
Second, we know that in the Scriptures, there are many modes and postures of prayer, but here the issue is not with the physical and outward posture of prayer, but rather with the inward posture of the heart.
To support this, Paul says that the men are to pray "lifting up holy hands" (1 Tim 2:8). What is interesting here is that the word "holy" is not the normal word "holy" in the NT (hagios). Rather it is, hosios which has the idea of "unpolluted" or "unstained by evil." Most think that when Paul speaks of 'hands' here, he is referring to the activities of life. Thus, the phrase here would have the idea of having an unstained life.
Third, Paul says, I want the men to pray (2:8). The word for "men" here is not the generic anthropos (a human being, mankind, etc), but rather it is aner (which always refers to a male gender as opposed to a female). Thus, Paul says that he "determines" (from the Greek word boulamai meaning to determine or command) that men do the praying. We must remember that the context of this chapter is in church life. Remember the theme verses of the book of 1 Timothy:
1 Timothy 3:14-15 14 I am writing these things to you, hoping to come to you before long; 15 but in case I am delayed, I write so that you may know how one ought to conduct himself in the household of God, which is the church of the living God, the pillar and support of the truth.
Thus, we are in the context of the local church. This also finds support in chapter three where Paul commands Timothy to appoint elders and deacons in every individual church body.
The point is this. Biblically speaking, men are the leaders of the church when the church meets for corporate worship. When the church is gathered together in a public venue, it is the men who are to do the praying (1 Tim 2:8). It was the same with the Jews when they would gather in synagogues. A woman would never be permitted to pray in public, it was the man's doing. It is the same concept here. Thus, when Paul says, I want the men to pray "in every place" (2:8), this phrase "in every place" is used four other times in the NT (1 Cor 1:2; 2 Cor 2:14; 1 Thess 1:8 and here). All four of these occurrences all have the local church assembly in mind.
In conclusion, may the Lord give us:
1) Fervency in prayer.
2) Holy lives so that we may pray without reproach (cf. 1 Peter 3:7).
3) Men to step up to spiritual leadership in the local churches.