These are my expressed opinions on this topic and not necessarily doctrines taught by the LDS faith, however there are links to very helpful articles that explain more in-depth what I am summarizing.
As members of the Church of Jesus Christ of Latter-Day Saints we believe that families are essential to Gods plan for us. Read The Family: A Proclamation to the World to understand a little more on this. As part of his plan God wants us to return to him again. This is done by following his Gospel, which includes, Baptism by proper Priesthood authority and receiving essential temple ordinances. These ordinances are done while we are alive on this earth, however many have passed on without this opportunity. This is why we do temple work, to give those that have passed without being baptized by proper Priesthood authority and receiving essential temple ordinances. We do the family history research to find our ancestors, learn of them and then act as proxy (in their place) for them to ensure that they essential ordinances are done properly.
Here is a picture of the LDS temple in Salt Lake City, Utah
Some might look at this and think that Mormons are just trying to convert everyone to their religion. Anger may even arise as you think that this is disrespectful to those who have passed on and where comfortable in their own religion while they were alive. However this is not the case. Just because these ordinances are being done on their behalf does not automatically mean that they are LDS. We believe these ancestors have the right to accept or deny these ordinances in the after life. We believe they are being taught and learning even after they have passed. Choice and Agency is essential in our doctrine.
Here is a quick article showing the guidelines set forth when submitting a name to be done in the temple. As you can see there are precautions and step taken to ensure that we are careful in who we are doing temple work for and how we do it.
I hope this help clear up some misconceptions about LDS members and Family History. We believe this is an important work and that it is essential for ourselves and our ancestors. Below I will attach several more articles if you have more concern or questions.
Helpful Links in relation to LDS Family History and Temple work