I believe that the unit was not meant to mean anything. It's just used as a conversion factor between metric and imperial measurements of exhaust velocity.
However, this confusing mess comes from the wikipedia article on specific impulse. Specific impulse is definitely meant to be a just conversion factor, but maybe there's another meaning you can get from it?
While the unit of seconds can seem confusing to laypeople, it is fairly simple to understand as "hover-time": how long a rocket can "hover" before running out of fuel, given the weight of that propellant/fuel. Of course, the weight of the rocket has to be taken out of consideration and so does the reduction in fuel weight as it's expended; the basic idea is "how long can any given amount of x hold itself up". Obviously that must mean "...against Earth's gravity", which means nothing in non-Earth conditions; hence Isp being given in velocity when propellant is measured in mass rather than weight, and the question becomes "how fast can any given amount of x accelerate itself?"
I've read that passage many times and still don't fully understand what its trying to say. Everything I say beyond this point is pure speculation based on my limited understanding of physics.
Let's say you have a rocket with infinite mass ratio (basically, all of the rocket mass can be used as propellant, this is theoretically the most efficient chemical rocket possible). In that case, the exhaust velocity will be equal to the delta-v of the ship (more on that if you don't know what I'm talking about). In a logarithmic funtion, as x (mass ratio) approaches infinity, y also approaches infinity (delta-v)
So as an example, a theoretically ideal rocket with an Isp of 400s will have a delta-v of 3443.5m/s. If you divide 3443.5m/s by 9.81m/s2, you'll of course get 350 seconds, which is the amount of time it would take a constant force to bring an object travelling at 3443.5m/s to a complete stop if it were able to subject it to a continuous deceleration. This means that if this theoretically ideal rocket were to hover at the surface of the earth, it would be able to do so for exactly 350 seconds, assuming the thrust pushing it up is equal to the gravitational force pulling it down.