Can anyone explain the idea of anodic nerve stimulation?
Short answer
Both anodic and cathodic current pulses can evoke neural activity, as shown in your image.

Background
You have to be aware that the current direction is arbitrary and the 'convention' you mention depends on your discipline. In electrophysiology, the anode is generally considered to be the positive electrode, the cathode is generally the negative electrode and the anode the positive. In physics however, current is assumed to be positive (due to historical reasons) and therefore the definition of anode and cathode is opposite. 

Secondly, there is no reason to assume that nerves under the cathode are stimulated (and not under the anode), as is shown in your picture - in both cases a neural response is elicited. For example in cochlear implants, biphasic current pulses are used, because these are safer than simple anodic or cathodic pulses. Biphasic pulses are charge balanced and consist of an anodic phase and an opposite cathodic phase. (Cochlear implants are arrays of electroides implanted in the inner ear that stimulate the auditory nerve directly and are used to treat sensorineural deafness).

In animals and humans, both anodic and cathodic pulses can evoke neural responses. In human cochlear implant users, the anodic phase is more effective than the cathodic phase. In contrast, in animals usually the opposite is observed. The reason for this discrepancy is unclear (Machery &amp; Cazals, 2016).

Whatever the exact reason of their differing effectivity in evoking neural activation - both anodic and cathodic current pulses can evoke neural activity. 

Reference
- Machery &amp; Cazals, Adv Exp Med Biol (2016); 894:133-42