Firstly: 

It is proven that the Prophet (blessings and peace of Allah be upon him) enjoined doing wudoo’ after eating camel meat, but he did not explain the reason why. We know that Allah, may He be glorified, is Most Wise and All Knowing, and He does not prescribe anything for His slaves except that which is good and is in their best interests in this world and the Hereafter, and He does not forbid to them anything but that which is harmful for them in this world and the Hereafter. 

What the Muslim should do is accept the commands of Allah, may He be glorified, and His Messenger (blessings and peace of Allah be upon him) and act upon them, even if he does not know the exact reason behind them. Similarly, he has to refrain from that which Allah and His Messenger have forbidden, even if he does not know the exact reason behind it, because he is a slave who is commanded to obey Allah and His Messenger (blessings and peace of Allah be upon him). He was created to do that, so he has to obey and submit, whilst believing that Allah is Most Wise and All-Knowing. If he finds out the reason behind it, then that is good upon good. 

End quote from Majmoo‘ Fataawa ash-Shaykh Ibn Baaz (10/157 

Secondly: 

Some of the scholars are of the view that this ruling is the matter of worship and the reason for it is not known. 

Al-Mardaawi (may Allah have mercy on him) said: The correct view is that doing wudoo’ after eating camel meat is an act of worship; this is the view of our companions … And it was said that there is a reason for it.

End quote from al-Insaaf, 1/355 

The scholars who said that there is a reason for it mentioned a number of reasons, including the following: 

1.The camel has a devilish nature, so whoever eats its meat will develop some devilish energy as a result; so it is prescribed to do wudoo’ so as to take away that energy.

It was narrated that al-Bara’ ibn ‘Aazib (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) was asked about praying in camel pens. He said: “Do not pray in camel pens, for they are of the devils.”

Narrated by Abu Dawood, 493; classed as saheeh by al-Albaani in al-Irwa’, 176 

According to a version narrated by Ibn Maajah (769): “…for they were created from the devils.” 

It was narrated that Hamzah ibn ‘Amr al-Aslami (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “On the back of every camel there is a devil, so when you ride them, mention the name of Allah, may He be glorified and exalted…”

Narrated by Ahmad, 2667; classed as hasan by al-Albaani in as-Silsilah as-Saheehah, 2271 

Shaykh al-Islam (may Allah have mercy on him) said: The Prophet (blessings and peace of Allah be upon him) indicated that camels are of the devils, meaning – and Allah knows best – that they are of the type of the devils, because every stubborn, rebellious creature is a devil, no matter what animal it is. So the black dog is a devil, and camels are the devils of the an‘aam animals (a category that includes camels, cattle and sheep), and there are also devils among mankind… So if a person eats camel meat that may make him hostile and wild, and cause him to acquire some characteristics like those of Shaytaan. The Shaytaan was created from fire, and fire is only extinguished by water, so man is enjoined to do wudoo’ after eating its meat so as to stop that devilish energy and suppress it. That is because the heart and attitude of man is changed by the food that he eats.

End quote from Sharh ‘Umdat al-Faqeeh, 1/185 

He also said:

If a person does wudoo’ after eating camel meat, that will extinguish the devilish energy and will put an end to any negative consequences, unlike the one who does not do wudoo’ after eating it, and he will see negative consequences. Hence it is said that because the Bedouin eat camel meat without doing wudoo’ after eating it, grudges developed among them. 

End quote from Majmoo‘ al-Fataawah, 20/523 

Similar comments were made by Ibn al-Qayyim (may Allah have mercy on him) in I‘laam al-Muwaqqi‘een ‘an Rabb il-‘Aalameen, 2/40

2.Camel meat has a strong impact on the nerves and provokes them. Hence modern medicine tells the hot-tempered individual not to eat a great deal of camel meat. Doing wudoo’ soothes and calms the nerves. By the same token, the Prophet (blessings and peace of Allah be upon him) instructed us to do wudoo’ at times of anger, so as to calm down.

End quote from ash-Sharh al-Mumti‘, 1/308 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: Whether this is the reason behind it or not, the reason is that it is the command of the Prophet (blessings and peace of Allah be upon him), but if we find out the wisdom behind it, that is a blessing from Allah and an increase in knowledge; if we do not know it, then we have to accept and submit. End quote. 

And Allah knows best.