The answer comes from relativity so I'll give you Edward Purcell's explanation. Imagine a wire with a current moving through it. Since the current is moving steadily the wire is neutral. Now let's say your positively charged particle is moving along at the same speed as the current. If we only knew of electric fields and had never read anything about magnetism, we would say there is no force here. However, now imagine the positive particle is at rest. We know from relativity that objects in motion appear shorter to observers at rest. Since the electrons (negative particles) are moving and the positive particles are not, the electrons will appear closer together from the point of view of the positive particle. Therefore, even though we know the wire is neutral, our friend the positive particle will see a negative charge and be attracted to it as it would to any negative electric field.
Einstein said that a force in one reference frame must exist an another, so the two are one and the same. This is why we use the term electromagetism. Depending on how fast the particle is moving, it can see only an electric field or a combination of an electric and magnetic field. This may be hard to visualize so check out the book by Purcell if you have trouble.
