So the little car light that you see blinking is the factory "Immobilizer" system the light indicates that the Immobilizer module is active and the vehicle cannot be started without the correct key. When you stick the key into the ignition, the Key Detection Antennae around the lock cylinder picks up the RFID chip's ID that is embedded in the key. The antennae transmits this data to the Immobilizer Module which determines if it is a valid key ID that matches what is stored in it's memory. If the key is valid, it then transmits a signal to the ECM to allow it to turn on the injectors when you crank the vehicle and turns off the security light (it will stop blinking when a valid key is inserted into the ignition.) That is how the standard factory security system works, you could add an additional module that gave you additional security features such as a glass break sensor, flashing lights and horn, ect. But that is a plug & play module that is installed by the dealer and has no additional indicators.
What you have is an aftermarket "Dealer/Port" installed alarm, basically it's a cheap, usually Code or Guardian alarm that's been installed before the vehicle is sold so they can raise the price by saying it has an "alarm system." They basically tap into a bunch of wires for the door locks and such with T-Tap clips; the only wires they cut are the ignition wire to prevent the vehicle from cranking (which really wouldn't matter since the Immobilizer system does a better job than these cheapo units.)