What exactly is basicity? In my textbook, it’s given that the trend of the basicity of the elements of group 15 is $$\ce{NH3 &gt; PH3 &gt; AsH3 &gt; SbH3 \ge BiH3}$$
Also, it’s said that the reducing character decreases down the group. (Which is the ability to lose $\ce{e-}$)
It’s also give (on a different page) that $\ce{H3PO3}$ and $\ce{H3PO4}$ are di- and tri-basic respectively. 

Phosphoric acid (presumably, a Brønsted-Lowry base) has a basicity of 3. This would imply that basicity is a property of acids. However, Ammonia (which is a Lewis base) has the highest basicity. Further, quickly Google search of the definition of basicity states: “Basicity is the number of hydrogen atoms replaceable by a base in a particular acid.” 

My question is, how does Ammonia (a Lewis base) have a basicity (i.e. acid character)... shouldn’t it be a weak base? Or is my understanding of the definition of basicity wrong?
The issue is that basicity has a couple of meanings and you have to be able to tell from the context what it means.

The first is logical, and is used to describe how basic a base is. That is the trend that you mentioned about the Group 15 hydrides. (In my experience, this is by far the more common usage of the word.)

The second is somewhat confusing, and it is used to describe how many protons of an acid can be removed by neutralisation with base. For example, $\ce{HCl}$ has one acidic proton, so it is monobasic; $\ce{H2SO4}$ has two acidic protons, so it is dibasic.