Mass units are arbitrary; use whatever you like, as long as you're consistent. Similarly, Velocity units are arbitrary; the delta-V computed will be in the same units. Specific impulse is in seconds.
A good explanation of delta-V is given in Chapter 2 of Space Settlements: A Design Study. The diagram to the right is based on Figure 2.2 of this book, and indicates the delta-V needed to transfer among various orbits.
Specific Impulse is exhaust velocity divided by g, the acceleration due to gravity on Earth's surface (9.80665 m/s^2). It's a common measure of the "mass efficiency" of a rocket engine. You can use the radio buttons above to convert between specific impulse and exhaust velocity.
The above calculator is very simplistic; it assumes no drag, and it allows only a single burn. But it can be applied to a great many models. For example, you could calculate the delta-V attainable by a baseball pitcher, throwing baseballs to change his orbit. Or, if you know the delta-V between an asteroid orbit and Earth orbit, you can calculate how much mass you'd have to eject from the asteroid to park it (which of course depends on how fast your mass launcher is).