What does pH of NH3 solution refers to?
As Ivan Neretin said in the comments, $\ce{H3O+}$ is already there, via the autodissociation of water:

$$\ce{2H2O &lt;=&gt; H3O+ + OH-}\tag{1}$$

Now water reacts with the ammonia that you add, according to the equilibrium reaction you provided:

$$\ce{NH3 + H2O &lt;=&gt; NH4+ + OH-}\tag{2}$$

This increases the hydroxide concentration further, so the first reaction is out of equilibrium, and consumes some hydronium and hydroxide by going in the net reverse direction, increasing the pH.

Alternatively, you can combine the two reactions to show that adding ammonia will lower the hydronium concentration:

$$\ce{NH3 + H3O+ &lt;=&gt; NH4+ + H2O}\tag{3}$$

All three reaction and the reverse reactions will occur simultaneously.


  However I don't fully understand what does pH mean, since in this dissociation there aren't any H3O+ molecules.


For basic solutions, the hydronium ion is a minor species. For acidic solutions, the hydroxide ion is a minor species. Sometimes in calculations, we get away with ignoring a minor species for a while, but they are still there.