In a constant magnetic field throughout space, a charged particle undergoes circular or helical motion. But if the field curves as shown, WHY will the particle 'follow' the field?
You can split the motion of the particle into two components: component parallel and perpendicular to the magnetic field.
If the magnetic field were uniform (constant magnitude and direction doesn't change), the particle would be making circles in the plane perpendicular to the direction of the magnetic field. It also continues to progress along the parallel direction of the magnetic field. This causes a helical path.
Apply the above reasoning to your question. The direction of the magnetic field is changing but the particle will always tend to form circles in the plane perpendicular to the direction of the magnetic field. Therefore, plane where the particle circles appears to be moving along the magnetic field.