Transit apps are mobile apps which help users get around in urban areas where car ownership may be low or traffic may be prohibitive to driving or parking.
A transit app may include integration with ridesharing services such as Uber and Lyft, bikesharing services, metro systems (subway, ferry, bus), as well as local taxi services.
Google pioneered transit trip planning in Portland , Oregon through a partnership with TriMet in Dec 2005.  It would be integrated into Google Maps two years later,  and make its way into the iPhone 3G in July 2008.
With smartphones becoming prolific, other app developers began to work on dedicated transit apps for both iOS and Android. When Apple removed Google Maps from the iPhone in 2012--including the built-in transit directions, many users turned to dedicated transit apps. 
The three most widely used transit apps across the world's cities are:
Moovit (80 countries)
Transit App (12 countries)
CityMapper (21 countries)
All three apps incorporate live service data in most large cities to alert users if--and why--their bus is running late, as well as live step-by-step modes which can alert the rider when to pull the stop cord, when to get off their bus, and automatic replanning if they miss their bus (or are likely to miss their next transfer point, based on the user's GPS location).
Some apps or websites such as Rome2Rio include more transportation modes (national rail, charter buses, flights) as well as price comparing between these different options, focusing on planning trips ahead of time and helping the user purchase passes or tickets, rather than live step-by-step directions during the trip.