For this kind of thing it's helpful to think about the dimensions and units involved.
In mechanics, "impulse" is a word for a unit of momentum. Momentum has dimensions (Mass * Speed), or (force * time), and can be stated in units of Newton-seconds.
"Specific" impulse is simply Impulse per unit mass of fuel (i.e. Newton-seconds per kilogram). The convention of stating it in units of seconds is based on Earth gravity (Newtons per kilogram).
If a system has specific impulse of 100 seconds, 1 kilogram of fuel would be able to accelerate a mass of 1kg at an acceleration of 1 G, for 100 seconds.
If I'm thinking about this correctly, the potential energy in the fuel isn't changing the net kinetic energy of the total mass, it's just re-distributing it between the vehicle and the exhaust.
Total momentum is conserved, but distributed: the individual momentum of the vehicle and the exhaust jet will be of equal magnitude and opposite direction (assuming a straight line), so if the rocket started in free space at rest (zero momentum), after it's run for a while the exhaust jet and vehicle will have equal and opposite momentum vectors.
Energy is a different thing, but related to specific impulse. In a perfectly efficient system (not what really happens), the decrease in stored energy within the fuel tanks would be equal to the increase in total kinetic energy (i.e. the sum of vehicle and exhaust kinetic energy).
In mechanics, "impulse" is a word for a unit of momentum. Momentum has dimensions (Mass * Speed), or (force * time), and can be stated in units of Newton-seconds.
"Specific" impulse is simply Impulse per unit mass of fuel (i.e. Newton-seconds per kilogram). The convention of stating it in units of seconds is based on Earth gravity (Newtons per kilogram).
If a system has specific impulse of 100 seconds, 1 kilogram of fuel would be able to accelerate a mass of 1kg at an acceleration of 1 G, for 100 seconds.