Daniel 1:15-21

Daniel 1:15
And at the end of ten days their countenances appeared fairer and fatter in flesh than all the children which did eat the portion of the king's meat.
When the time of testing had ended, Melzar then made an inspection of the four men.  What he had seen pleased him because they looked much healthier than the men who ate the King’s portion.  When the verse states they looked fatter in flesh, it doesn’t mean they had serious weight gain but they looked healthier in appearance than the others.
Daniel 1:16
Thus Melzar took away the portion of their meat, and the wine that they should drink; and gave them pulse.
So Melzar seeing the results of their requested diet had taken away all the rich foods from them and gave them pulse, which was their request.  Melzar let them continue their diet since it made them of better countenance than the others and he would probably win favor with the King seeing them in such good and healthy condition.
Daniel 1:17
As for these four children, God gave them knowledge and skill in all learning and wisdom: and Daniel had understanding in all visions and dreams.
Here we read that God had specially endowed them with knowledge and skills.  God may have allowed them to understand the Chaldean language much quicker.  God also gave them wisdom which was the ability to apply what they learn in the Scriptures to their particular situation being advisors to the King.  Since they were now in Babylon, they would have also been skilled in learning the literature and customs of Babylon so they would be able to do their jobs more effectively.  At this time, before the completion of the Bible, God was still communicating with His people through dreams and visions.  Just like Joseph whom God gave the ability to understand and interpret dreams, Daniel and his three colleagues were given that same ability.  It would save the lives of many people in the future.  It was also necessary because God was going to give them the true interpretations of any dreams they were asked to interpret since the Babylonians had relied heavily on astrology, divination, and the occult.  All of which were useless in obtaining truth since the source of these was Satan.
Daniel 1:18
Now at the end of the days that the king had said he should bring them in, then the prince of the eunuchs brought them in before Nebuchadnezzar.
Now it was at the end of three years that Daniel, Azariah, Hananiah, and Mishael were to be brought before the King.  Their time of preparation was now over and it was time to meet the King who would assign them their positions in the government.  This is why it was so important for them to learn the Babylonian language and customs so they could intelligently approach the King.  So Ashpenaz brought them in before the King and I am sure he was probably feeling good since they looked real good and were well studied.
Daniel 1:19
And the king communed with them; and among them all was found none like Daniel, Hananiah, Mishael, and Azariah: therefore stood they before the king.
Once they were in with the King he began to speak with them and it seems in the course of the conversation that the King declared that Daniel and his three colleagues had no equals among the captives, in fact, the compliment was probably extended to the King’s homegrown counselors who were less wise than the four.  The wisdom and understanding which God gave them allowed them to be brought into the presence of the King.
Proverbs 22:29 (KJV)   Seest thou a man diligent in his business? he shall stand before kings; he shall not stand before mean men.
Daniel and his companions showed a diligence in wanting to serve the Lord that their diligence also allowed them to stand before Kings which was written by Solomon about  4 centuries prior to this meeting.  It is a great principle for Christians to follow since they will also reap the same benefits of that wisdom.
Daniel 1:20
And in all matters of wisdom and understanding, that the king inquired of them, he found them ten times better than all the magicians and astrologers that were in all his realm.
Already you can see the roots of jealousy being planted, they became the King’s preferred counselors over those who were born native in Babylon.  The understanding can also be understood as discernment in many matters.  God gave them such tremendous wisdom and understanding that they had the ability to stand before the King and become his favorite counselors.  The other counselors were native born but Daniel and his three friends were only in Babylon for three years at this time and curried greater favor with the King in place of his other counselors.  This shows the difference between Godly counsel and the counsel which is based in the occult arts.   Worldly counsel is based on satanic input.  Daniel and his friends were considered ten times better than the occult based counselors.  The “ten times” indicates that they were superior to the other counselors.
Daniel 1:21
And Daniel continued even unto the first year of king Cyrus.
Daniel had served for a period of about 70 years.  He was brought to Babylon in 605 B.C. by Nebuchadnezzar and King Cyrus of the Meds and Persians had captured Babylon in 539 B.C. in which he continued to serve King Cyrus.