The 7th article of Faith reads:
7 We believe in the gift of tongues, prophecy, revelation, visions, healing, interpretation of tongues, and so forth.
Gift Of Tongues and Interpretation of Tongues
What the heck is the gift of tongues and the Interpretation of Tongues? Everyone has a tongue in their mouth right? Well that not exactly what this is about. According to the LDS churches website (www.lds.org) the church believes:
"A gift of the Holy Ghost that allows inspired individuals to speak in, understand, or interpret unfamiliar languages."
So the gift of tongues (and the interpretation of them) is really about tongues, since we use our tong differently depending on the language we speak. Members of the LDS church believe that, when needed, Heavenly Father will provide individuals the ability to speak in languages that are not native to that person. Our missionaries are a great example of this. In a few weeks at one of the churches MTC's (missionary training center) young men and women learn the language they will speak for the next 18024 months. After a few weeks they are sent to the country where they will stay and are expected to be able to communicate with the people of that country - in their language.
Prophecy, Revelation and Visions
You could write books about prophecy, revelation and visions (and frankly many have been) so I really didn't want to spend a ton of time in this area, since when you read this Article of Faith tongues is what jumps out at you.
Basically members of he LDS church believe that the heavens are still open and that the opportunity for us as individuals and collectively as Gods children is still there. Many religions teach that God is done and will not share anymore with his children. I personally believe God has so much left to teach us as his children as well as providing us direction that he's just chomping at the bit to revel things. I think the biggest problem is us as individuals we are not ready to receive the revelation that we need at that point in our life. Sometimes we are not worthy but mostly we just aren't listening.
Healings and Other Miracles
I think anyone who believes in Christ believes in healing. After all the 4 gospels are full of stories of Jesus healing various people with various aliments. But the bigger question is, do these things continue today? The short answer is yes they do.
In the LDS church we believe that the priesthood (which is the authority to act in Gods name) is alive and functioning. We believe that through the authority of the priesthood the power of God can be called upon and people can be healed by their faith.
Does that mean that healings and other miracles require the priesthood? Of course not, because with faith "nothing shall be impossible" (Mathew 17:20). Miracles happen all the time. A group of people come together and pray and a child is healed. Someone misses getting injured in an accident, or even some of the shots I make on the basketball court could be considered miracles. Really we have to understand that God is alive and is mindful of us. He is there to help us and if we call upon him, he will deliver.
To conclude my thoughts here, God provides his children many gifts. These gifts are given for different purposes and to different people. There is always one goal which is to bring to pass the immortality and eternal if of man.