This may be due to loose rear-wheel bearings. They may just need to be adjusted.

However, your spokes are severely undertensioned. I can see at least one that has zero tension. The wheel may have previously been damaged into a taco shape and was trued back to look straight with vastly varying tensions. I suggest having a shop adjust the bearings (or learn to do it yourself). Then tighten up all the spokes evenly. If you squeeze two parallel spokes with your hand as hard as you can, they shouldn't bend together any more than 4-5mm. I suspect yours will move 10-20mm.

Here's a good site showing how to adjust hub-bearings: Park Tool - Hub Overhaul & Adjustment