When the Holy Ghost comes to be with us, we can feel it. It's a sweet, peaceful, warm feeling of power, sometimes barely noticeable and sometimes like a fire burning in our hearts, and it makes us feel loved and happy. The way the Holy Ghost feels is so wonderful that it alone can make a person cry just from sheer joy. It's pretty cool. When the feeling that the Holy Ghost gives us is accompanied with a reassuring feeling that whatever we were thinking about is true, that new knowledge can produce strong emotion. For example, if you were praying to God about whether the Bible is true or not, and you suddenly felt the Holy Ghost reassuring you that yes, it is true, then you would know that you no longer have to worry about believing in something that isn't actually true. You could then move forward with confidence that to read the Bible would put you on the right path. That new knowledge would make you feel relieved, confident, and maybe a little less stressed out.
Mormons are truth-seekers. We believe that each of us needs to find out if God is real, and if he is, what he wants us to believe and to do. Most Mormons have investigated the possibility of there being a God and have felt the Holy Ghost confirming to them that yes, God is real. We have also made it priority to find out what it is that God wants us to believe and to do. That's why when you go to church and hear Mormons talk about their beliefs, they will get emotional as they remember the times when the Holy Ghost came to them and testified of specific truths. They may also get emotional because they are feeling the Holy Ghost again as they are talking, reinforcing their testimonies of the truth.
The feelings inspired by the Holy Ghost are beautiful and can make us cry, but sometimes we cry out of emotion alone and not because of the influence of the Holy Ghost. Our church services tend to get very personal as we share stories from our own lives. We all experience really painful challenges, and many Mormons feel comfortable enough to share them and to share the lessons God taught them because of those experiences. Some of us will cry as we remember pain, and some of us because we're particularly passionate about something, and some of us just because we have trouble regulating our emotions. Keep in mind that strong emotion doesn't necessarily indicate the influence of the Holy Ghost or that whatever is said is true.