Probably the same reason as why OSRM is faster than pgRouting: because it uses pre-calculated routes.

pgRouting allows you to change conditions in real time. Does your phone app allow you to do that? Like, for example, add traffic data and recalculate the route depending on this new data?

By the way, your igoApp does not seem to use offline data, are you sure it does not ask a remote server? http://www.igonavigation.com/igo-my-way-for-iphone

Probably because it uses pre-calculated routes.

As an example of an open source routing app with pre-calculated routes, OSRM uses contraction hierarchies to create shortcuts: http://algo2.iti.kit.edu/routeplanning.php

PgRouting just creates the relations between source and target with the pgr_network_topology function. http://workshop.pgrouting.org/chapters/topology.html

pgRouting allows you to change conditions in real time. Does your phone app allow you to do that? Like, for example, add traffic data and recalculate the route depending on this new data?