Why is there a maximum altitude to restart a jet engine?
Basically, it gives the pilot the altitude and airspeed at which the engines can be relighted in flight. Based on these values, the pilot has to take a decision to descend etc. A jet engine requires (compressed) air, fuel and a flame source for (re)starting. So air density plays an important part in determining the maximum restart altitude.
In addition, there are other factors at play as well. In case of unassisted (without APU, for example) windmill restarting, the airspeed must be enough to overcome the inertia of the components. In certification memorandum on Turbine Engine relighting in flight, EASA says,

.. as core - bypass ratio of engines continues to increase,  higher  airspeeds  are  generally  required  to  enable  unassisted  windmill   restarting.  The  inertial  effects  because of the increased size, mass,  and number of engine driven gearbox accessories may also contribute  to   increased  rotor  drag  loads,  decrease  starting  performance,  and   possibly  contribute  to  rotor-lock  conditions.

In case a starter is available, the airspeeds required go down (as APU itself is usually a small turbine, the altitude effects are not as pronounced). According to CFR § 25.903 Engines:

(2) An altitude and airspeed envelope must be established for in-flight engine restarting, and each engine must have a restart capability within that envelope.
(3) For turbine engine powered airplanes, if the minimum windmilling speed of the engines, following the inflight shutdown of all engines, is insufficient to provide the necessary electrical power for engine ignition, a power source independent of the engine-driven electrical power generating
system must be provided to permit inflight engine ignition for restarting.

The engine restarting envelope is decided both in terms of altitude and airspeed. It also depends on aircraft. For example, in ETOPS aircraft, the APU must be designed to have airstart capability throughout the normal flight envelope. Regarding this envelope, EASA says,

2 Envelope of Altitude and Airspeed
2.1  Sufficient flight tests should be made over the range of conditions detailed in 2.2 and 2.3, to establish the envelope of altitude and airspeed for reliable engine restarts... The effect of engine deterioration in service should be taken into account.
2.2 Altitude and Configuration. From sea-level to the maximum declared  restarting altitude in all appropriate configurations likely to affect   restarting, including the emergency descent configuration.
2.3 Airspeed. From the minimum to the maximum declared airspeed at all altitudes up to the maximum declared engine restarting altitude. The airspeed range of the declared relight envelope should cover at least 30 kt.