In that time, Arabs were divided into tribes and that was pretty much everything determining their lives. You can think that a tribe is a one big family.
For example, if you take a wife within your tribe and someday her brother sweared to you, what would you do? A slap or a punch maybe. If he beats you, then the elders of the tribe would solve it. In this case, it does matter who was actually right.
Now, think that someone without your tribe sweared to you. What would you do? A slap or a punch probably. But this time, the issue between you two would become bigger. Doesn't matter which one of you was right, your tribe would stand behind you and his tribe would stand behind him. 2-men-fight would easily become 100-men-fight. In this fight, probably at least 1 man would be killed. Then this little conflict would become a blood vengeance.
Blood vengeance is something like this: It starts with killing somebody in different tribe. Then that tribe kill somebody in your tribe in order to take revenge. Then somebody in your tribe kill somebody at other tribe for revenge. This goes on and on. At that time, nearly all of the tribes has blood vengeance between each other.
This is important: there can't be a blood vengeance inside the tribe.
How to stop this paradox? The most well-known way to stop blood vengeance is to marry a man from this tribe with a woman from other tribe. With this marriage, these two tribes would somehow unite, thus you can't maintain a blood vengeance inside one tribe.
Mohammad(puh) united major tribes in that area with marriages. To do this, not only himself, but also his close friends did the same thing. They tightened the bonds between tribes and put an end to this blood vengeance tradition. You can't kill your wife's brother just because he sweared to you, right?
Head of a State
Kings at that time, didn't read messages unless it is signed by an official leader. After sometime, the tribes mostly united and thus Mohammad(puh) had become a state leader. Then he started to send messages to known other states's leaders to invite them and their communities to Islam. He send other messages to them about the relationships between states.
At that time, one tradition between kings was to send woman slaves to each other in order to say I am good with you. Rejecting this "gift" with any excuse would mean "I am not good with you" and would start a conflict. Some kings would count this rejection as a reason for war. When Mohammad(puh) had become the leader of the state, some kings sent slaves to him. Well, he couldn't reject, he couldn't keep them (he was poor at that time), and he couldn't say "You are free, go do whatever you want." (they may not know Arabic, they certainly don't know anybody on that area). He had to marry them, but I said he was poor, slaves were coming in groups of 5s, 10s etc. And there was a 4 wife limit.
Explaining Woman Private Issues to Woman
Islam determines a Muslim's private life including sex and woman monthly period. But a man can't easily talk to women about these issues. You can't talk about sex's limits with somebody's mother or wife, in this case, Mohammad(puh)'s wives did this job. They learned from the Prophet(puh) and explained to other women within talks without men.
With this verse, all of these problems were solved. The Prophet(puh) could unite tribes, could stop blood wars, could reach more woman to explain private issues and could solve slave issue. But, he had a limit too: 10 wives at the same time, can't divorce any of them in order to marry with another etc. He had to be very careful even in these circumstances. For example he freed and married 1 of the slaves who was sent to him, and send the others back, that was a proper excuse.