Subjective rights are relations between legal subjects that depend on the rule of law for their recognition and enforcement.
Subjective rights are closely connected with legal powers, the exercise of which change the set of rights and duties legal subjects hold and are subject to. For example, a property right in some good, such as a car, entails the legal power to dispose of it, for example by sale.
Subjective rights entail concomitant duties on one or more other legal subject(s). For example, when you purchase a car, the contract of sale attributes to you a right to receive the vehicle, as well as placing you under a duty to pay the agreed purchase price. By the same token, the contract places the showroom under a duty to supply the vehicle, but also gives it a right to receive the purchase price.
Subjective rights can be relative, existing between specified legal subjects, as in the example above of the contract between the purchaser of the car and the showroom. This is also known as a right ad personam – it is enforceable only between the purchaser of the car and the showroom.
Subjective rights can also be absolute, existing between a legal subject and all others, as in the right of the owner of the car not to have her possession of it interfered with, or her right as a driver to be treated with reasonable care by fellow road users. This is also known as a right erga omnes – it is enforceable by the owner or driver of the car against every other legal subject. Someone who tries to steal the car, or who damages it through negligent driving, infringes that right, and becomes liable to a court judgment requiring in the former case restitution of value and punishment, and in the latter the payment of damages.
In private law, subjective rights are horizontal between legal subjects, with the state ‘watching over’ as guarantor of the relationship and adjudicator of any dispute.
In public law, subjective rights are vertical between the legal subject and the state (although relationships with the state can be horizontal too, for example where a car manufacturer supplies vehicles to the government under a contract, in which case the state is acting in a ‘private’ capacity).
Fundamental rights are also subjective rights. For example, the collection of personal data by the various sensors in a (self-driving) car will be subject to the limits set by the fundamental right to data protection.