Megan! answered...

A testimony is the knowledge that a certain principle is true, right, or good. For example, I have a testimony that Jesus Christ is the Son of God, and that He did truly atone for our sins. In order to gain that knowledge, I have studied, reflected on what I learned in my study, and prayed to have that knowledge confirmed in my heart. As an answer to those prayers, (for there were many--building a testimony is an ongoing process) I have felt the truth in my heart.
We can gain testimonies of many principles. Another way is to put that principle into action, as sort of a test. In order to gain a testimony of prayer, we might try praying. To gain a testimony of the principle of tithing, we might try paying a full tithe. (10% of our income.) As we strive to live these principles, the Holy Ghost will confirm the truthfulness of them to our hearts. We will know that they are right; we will have a testimony of them.

Mormons also talk about "bearing testimony." This simply means to share the testimony we have gained with other people, either in a formal setting (like in church) or in a more informal setting (like in a conversation with a friend.)