[Ligander]

 What are definitions of "on-resonance" and "off-resonance" ?

 There is plenty of stuff on this topic in Internet but I haven't found any definitions of these terms.

 P.S. English is not my mother tongue and I afraid that for native speakers these terms are self-explanatory.

[arit]

At equilibrium the spins precess around the B0-field (z-axis) at their respective Larmor frequency,
and when we apply a 90-degree pulse, it causes the spins to precess in the x-y plane,
creating the observable magnetization.

The 90-degree pulse is actually another, weaker magnetic field that oscillates very rapidly.
If the frequency of this magnetic field is at, or close to the Larmor frequency of the spins
in the sample, we fulfill the resonance condition, and in effect "tilt" the spins 90-degrees
to the x-y plane.

If the frequency of the B1-field is far from the Larmor frequency ("off-resonance"), the spin doesn't
tilt all the way to x-y plane. This might lead to just getting less signal, but can also have other
effects.

For a far better and more rigorous explanation I suggest Spin Dynamics by Malcolm Levitt.
You might also want to take a look at a short video regarding the subject http://www.magritek.com/videos.html#01