Roughly speaking the electric field at a point is the force experienced by a unit positive charge at that point. In that sense, it is detectable in an experiment. If you keep a positive test charge in between a positive and a negative charge, the test charge would move away from the positive charge and towards the negative charge.
But we could have just as easily defined electric field as the force experienced by a unit negative charge. The directions would be reversed but the physics would be the same. In that sense, the direction is just a convention. But once it has been defined in one way, there is a definite physical way to measure the field and it's direction.