Application processor is a term used to describe pretty much every central processor that isn't a CPU (Intel) or an APU (Intel/AMD). SoCs (system-on-chip) is another term.
According to Digitimes Research, the global market for application processors will slow down.
It will still grow for a while, but not at the rates of previous years.
For example, while the 2013 increase was of 43%, the one projected for 2014 is of 23%, to go even lower in 2015.
It's because the smartphone market is maturing, which means that purchases are coming more from those seeking to upgrade their phone instead of buying a new one because they don't already have one.
Basically, of people who afford/are interested in owning a smartphone, the number of those who already own one (and,thus, aren't likely to buy another for a few years) is starting to exceed the number of people who still don't. Like it happened on the PC market and everywhere else.