When the Pharisees asked Jesus about divorce, He affirmed the pattern God established in the garden of Eden with Adam and Eve (Mt 19:1-6). This not only affirms that marriage is between one man and one woman, but the historical veracity of the book of Genesis. They then questioned why divorce was accommodated in the law of Moses. Jesus responded it was not because it was the will of God, but because of the hardness of their hearts. He then limited divorce to the cause of adultery (Mt 19:7-9). His disciples replied that if that was the case, it would be better not to marry. Jesus then spoke about eunuchs (Mt 19:10-12). He said there are three kinds of eunuchs. There are those that are born that way. There are those that men make that way, and there are those that make themselves that way for the kingdom of God.
So what is a eunuch? The word means a man who was castrated. Some men are born with reproductive problems. Priests who were damaged this way were not allowed to serve in the tabernacle (Lev 21:20, Deut 23:1). Other men were purposefully damaged this way so they would be dedicated to serving as officers to the king and not distracted with a family (2Ki 9:32, 2Ki 20:18, Est 2, Jer 29:2, Jer 34:19, Jer 38:7, Jer 41:16, Dan 1, Acts 8:26-39). The word was also translated chamberlain 13 times, and officer 13 times. In Esther 2, they were used as caretakers for the women. These were the men Jesus was talking about that were made that way by men.
What did Jesus mean when He said some men make themselves eunuchs for the kingdom of God? Is He advocating men purposefully damaging their bodies, and that would somehow make them better Christians? This does not mean that any more than Jesus meant that literally plucking out our eyes or cutting off our hands makes us better Christians (Mt 5:29-30). A man makes himself a eunuch in the context by declining, whether temporarily or permanently, the opportunity to get married so he can focus totally on serving God. Paul talked about this in 1Corinthians 7. A married person has additional earthly responsibilities that demand time, energy, attention, and other resources that a single person does not. Therefore some people can make that commitment to God, but it is not required (Mt 19:11-12, 1Cor 7:6 & 35). Women therefore can also be "eunuchs", which shows there are broader implications to the meaning.
There are various teachings about fasting - what constitutes fasting, different ways to fast, priorities in fasting, how to care for your health while fasting, how long to fast, etc. I believe God honors whatever sacrifice we do when it is according to the Bible, His will, and spiritual leadership. The same is true for other sacrifices we make. When we make a consecration to God and keep it, God will honor it. Married people can be "eunuchs" in that sense.
Numbers 6 speaks of the Nazarite vow, which was a temporary, special consecration one could make to God. It involved not cutting the hair, not partaking of any products of the grapevine, and not touching a dead body. A special ceremony would be performed at the end of the period of the vow, part of which was cutting the hair. Samson was to be a Nazarite his whole life (Jud 13:5). There is some evidence Paul may have taken this vow (Acts 18:18, Acts 21:23-24). We can all be "eunuchs" in some way by making a special consecration to God above the normal practice, whether temporarily or permanently. God will draw close to those who draw close to Him (Jam 4:8).
Some people perceive of themselves as spiritual eunuchs in that they have no power to produce fruitfulness, or to reproduce other disciples.. God also has a promise for you. You will no longer call yourself "a dry tree". If you keep the commandments of God and please Him, you are a child of God and have great place in His eternal kingdom which will never be taken away (Is 56:3-5).