This verse is from Luke 8, where He heals the dead girl:
Why would Jesus want His healing powers to be kept a secret?
Well, it's a matter of context. You have to read and understand the entire story. In the first part of this we see a ruler of a synagog, having faith and bowing in front of Jesus
in public.
Luk 8:40 And it came to pass, that, when Jesus was returned, the people gladly received him: for they were all waiting for him.
Luk 8:41 And, behold, there came a man named Jairus, and he was a ruler of the synagogue: and he fell down at Jesus' feet, and besought him that he would come into his house:
Luk 8:42 For he had one only daughter, about twelve years of age, and she lay a dying. But as he went the people thronged him.
Now we see that a servant of the house comes out and says not to worry about it, it's too late.
Luk 8:49 While he yet spake, there cometh one from the ruler of the synagogue's house, saying to him, Thy daughter is dead; trouble not the Master.
Luk 8:50 But when Jesus heard it, he answered him, saying, Fear not: believe only, and she shall be made whole.
In this, Jesus was speaking of the same kind of faith shown by the centurion shown in: (Mat 8:8-10), but the man did not have that kind of faith, so Jesus went to his house.
Luk 8:51 And when he came into the house, he suffered no man to go in, save Peter, and James, and John, and the father and the mother of the maiden.
Luk 8:52 And all wept, and bewailed her: but he said, Weep not; she is not dead, but sleepeth.
Luk 8:53
And they laughed him to scorn, knowing that she was dead.
They made fun of Jesus, laughing at him, thinking he was an idiot. Maybe even calling him one.
Luk 8:54
And he put them all out, and took her by the hand, and called, saying, Maid, arise.
An interesting parallel is the ending of Jesus's conversation with the centurion in: (Mat 8:11-13) It states that those with no faith will be "cast out".
Luk 8:55 And her spirit came again, and she arose straightway: and he commanded to give her meat.
Luk 8:56 And her parents were astonished: but he charged them that they should tell no man what was done.
This is an admonishment for disbelief. A rebuke for doubting in Jesus's authority over death. Why would you want an unbelieving scoffer to testify your miraculous deeds? Also, if you read the entire chapters surrounding this one event you will see there were people in the crowd wanting to do away with Jesus. With it not yet being the appointed time, he may have chose discretion in order to "keep the peace".