"Then they brought to Him one who was deaf and had an impediment in his speech, and they begged Him to put His hand on him. And He took him aside from the multitude, and put His fingers in his ears, and He spat and touched his tongue. Then, looking up to heaven, He sighed, and said to him, 'Ephphatha,' that is, 'Be opened.' Immediately his ears were opened, and the impediment of his tongue was loosed, and he spoke plainly. Then He commanded them that they should tell no one; but the more widely they proclaimed it. And they were astonished beyond measure, saying, 'He has done all things well. He makes both the deaf to hear and the mute to speak.'"
A man who was deaf and had an impediment in his speech was brought to Jesus for healing. It is reasonable to assume that the man had learned to speak before losing his hearing. Some have speculated that the loss in hearing caused the speech impediment, although it is impossible to know for certain from the context.
Jesus took the man "aside from the multitude, and put His fingers in his ears, and He spat and touched his tongue." Certainly Jesus separated the man from the crowd to avoid publicity. Jesus' actions here cannot be specifically explained, but in general they would assure this man that he was being healed. Usually Jesus would give assurance through His words, but such would do no good in the case of a deaf man. Interestingly, as in the healing of Jairus' daughter, Jesus spoke in Aramaic (cf. Mark 5:41). It is not stated as to why He sighed, but most likely it was a simple expression of sympathy.
The miracle was immediately performed and perfectly - "Immediately his ears were opened, and the impediment of his tongue was loosed, and he spoke plainly" (Mark 7:35). Jesus commanded that this great healing be kept a secret (in order to prevent Himself from being overwhelmed with requests for healing such as these, perhaps). Of course, those who were aware of the awesome work that had taken place would be challenged to keep a secret like this--and most seemingly failed. Jesus' humble request for silence regarding His miracles made Him seem even more wonderful to the people, which in turn caused them to be eager to spread the news.
The multitudes were "astonished beyond measure" (Mark 7:37). Everything Jesus was doing was amazing to them. It should be noted that Jesus was in a region that had formerly driven Him out (cf. Mark 5:17). Evidently their feelings for Him had changed over time. Perhaps the evangelistic efforts of the man formerly possessed by Legion were partly responsible for this pleasant change (cf. Mark 5:19,20). This is a lesson that should be learned by Christians today: sometimes people change over time for the better. Merely because one rejects the gospel today doesn't mean that he will always reject it. Some who had driven Christ out of the region may have later been astonished at His amazing works. Some who curse the name of God today may later have their hearts softened and become more receptive to the truth due to various circumstances.