I'm having moles or freckles start appearing out of no where. What does this mean?

Normal. These can represent seborrheic keratosis which are found commonly on the trunk. They appear after age 35 and may have a genetic component. They are removable if they disturb you cosmetically, .
New mole. Your body makes new moles and freckles as you age. The key is to use sun protection and have your moles and freckles examined routinely by a dermatologist.