A quick dimensional analysis ... km/s/Mpc has dimensions of (L/T)/L = T^-1 (L = length, T = time).

Or, in ordinary words, frequency. Which is measured in Hertz (Hz = inverse seconds).

Peter Wilson said as much, in line 2) above (though I get 2.3 x 10^-18 Hz, not -19).

It's a pretty deep frequency, wouldn't you say? About one beat per 13 billion years (if I've done my arithmetic right). Hmm, now where have I seen that number before?