A side cap is a fold-able military cap with straight sides, no brim and hollow crown which when worn forms a very distinctive shape.
In the UK its officially known as field service cap, in the US its called a garrison cap or flight cap.
The best feature of this cap is can easily be folded into a pocket, over the belt or under the shoulder strap of a military uniform.
This cap sports a Russian badge so probably from a Russian unit but since I found it at cat boot I no idea for sure.