Praise be to Allah (The Glorified and Exalted).
1) To understand the Qur'an, one needs to know the biography of the Prophet (peace and blessings be upon him) and what occurred during that time period.
2) One needs to understand how the Qur'an was revealed. non-Muslims think the entire Qur'an was revealed at once in a book format that the Prophet (peace and blessings be upon him) brought. The Qur'an was actually revealed in portions, verses revealed at different situations, sometimes to even answer questions, etc. And then the angel Jabriel (Gabriel) (peace be upon him) would recite the Chapters and verses as they now appear. The Prophet (peace and blessings be upon him) would memorize the verses and chapters and reveal them to the people. Some portions were written by some individuals, however, the Qur'an as it appears in book format now, was compiled into a book format under Abu Bakr's Caliphate (may Allah be pleased with him).
3) The verse you mention is in the following context:
"88) Then what is the matter with you that you are divided into two parties about the hypocrites? Allah has cast them back (to disbelief) because of what they have earned. Do you want to guide him whom Allah has made to go astray? And he whom Allah has made to go astray, you will never find for him any way (of guidance).
89) They wish that you reject Faith, as they have rejected (Faith), and thus that you all become equal (like one another). So take not Auliya' (protectors or friends) from them, till they emigrate in the Way of Allah (to Muhammad صلى الله عليه وسلم). But if they turn back (from Islam), take (hold of) them and kill them wherever you find them, and take neither Auliya' (protectors or friends) nor helpers from them.
90) Except those who join a group, between you and whom there is a treaty (of peace), or those who approach you with their breasts restraining from fighting you as well as fighting their own people. Had Allah willed, indeed He would have given them power over you, and they would have fought you. So if they withdraw from you, and fight not against you, and offer you peace, then Allah has opened no way for you against them.
91) You will find others that wish to have security from you and security from their people. Every time they are sent back to temptation, they yield thereto. If they withdraw not from you, nor offer you peace, nor restrain their hands, take (hold of) them and kill them wherever you find them. In their case, We have provided you with a clear warrant against them." [4:88-91]
Long story short, some people were hypocrites, meaning they called themselves Muslims, but secretly they were pagans and hated the Muslims. They wished to deceive the Muslims from within and lead them to destruction and support their enemies by giving them intelligence, etc. They posed a great risk to the lives of the innocent Muslims, so Allah (The Exalted) passed Judgment over them in these verses and permitted the Muslims to arrest and execute the leaders among them that posed this type of danger, except what is mentioned in the verse about the exceptions, such as those who don't mean physical harm to Muslims or live under the protection of other tribes that have peace with the Muslims, etc, which is made clear in verse 91.
This type of treatment of hypocrites or "traitors," which is the term used by modern governments, is something one sees throughout the world. For example, the U.S. also arrests and punishes its traitors with execution, which they have done in the past. Other nations throughout the world do the same. This atheist of yours also lives in a land in which his government behaves in the same manner, or else how could they protect their citizens from hostile forces from within and externally.
This response was long, and you wanted something short. However, there is no way to learn about Islam in the "short" and "quick" manner. One must read extensively to understand and become set in the religion, so when ignorant people, with the mindset and naivety of a child, thinking of the world with an idealist mentality, talk nonsense about the truth, you can clarify it for them. Now, as for some of these non-Muslims that quote these type of verses from the Qur'an, but have no real intention of learning the religion from extensive study. They are just a group of tricky-minded and deceitful people who wish to mislead the ignorant. Do not be surprised that they question everything in the religion from A to Z. This is because they do not take the time to learn on their own. Especially these atheists are among the most cynical group when it comes to religion. A man finds the truth after extensive studies and contemplation. Not from reading a verse here and there and thinking, "I am now an expert of Islam, with my lack of Arabic knowledge, lack of understanding of Islamic history, lack of fairness in my assessment, lack of understanding of political science and governing, lack of understanding in military sciences, etc."
Learn about Islam at the following sites:
1)
http://www.islamreligion.com/
2)
http://thedeenshow.com/
3) Read the thread "Proving Islam" :
http://www.turntoislam.com/forum/showthread.php?t=40837
4) Read "Science Against Evolution" and forward to the atheist:
http://www.turntoislam.com/forum/showthread.php?t=62132
5) And another post dealing with evolution:
http://www.turntoislam.com/forum/showthread.php?t=60168
And Allah (The Glorified and Exalted) Knows Best.