One reason for this back pain may be due to weak back muscles that are involved in sitting straight.
When people first start meditation practices, they may not be used to sitting up straight for long periods of time. Even sitting for short periods of time may cause slight back pain.
Once you progress with your meditation practice, the muscles involved in sitting with a straight back will get stronger, resulting in the ability to sit for longer in meditation without suffering from the back pain and discomfort.
Another positive side effect is that you may have improved posture in your day-to-day life as well. The reason for this is that when you meditate, it's important to sit with a straight back, and not to be hunched. You are actively and mindfully training and adjusting your posture and making sure you are sitting with a straight back. This posture training does not benefit only your meditation sessions, but your daily life as well. You will start to notice that you are being more mindful of your posture. As you progress, you will start to have better posture without even trying or forcing it, it will just be natural.
One way to help strengthen your back muscles to prevent the pain and discomfort is to include some physical activities in to your schedule, such as weight training or yoga. If your goal is just to be able to sit longer in meditation without experiencing the back pain, you won't need to lift very heavy weights or go to any extremes. Just being physically active and strengthening the back and surrounding muscles should be enough.
Don't skip your core!
Your core muscles are another important element in having good posture, this goes for sitting and meditating as well. Try to include some core exercises to help ensure that you are strengthening the muscles involved in keeping a good posture. This can really help make the pain and discomfort go away.