The R-PI has on its GPIO header:
8 GPIO parallel I/O pins, that can control:
* Dynamite sticks
* heating elements
And thousands of other things, and as inputs can read (detect)
* Switches and pushbuttons
* light levels shining on LDR's
* Status signals from digital devices
* Water levels
* trip wires
* Rocks thrown into ponds.
And millions of other slightly digital input signals (with help from the right sensors)
It also has a UART (Universal Asynchronous Receiver Transmitter) (actually it seems to have several), which can be used for bidirectional communication with a zillion other devices and micro-controllers, for keyboards, mouse, joystick and not to forget via a level converter to RS232 signals. Probably the most useful use will be to control arduino's, used as "real time interface controllers".
It has I2C (inter IC bus) useable (as the name implies) to connect to all kinds of digital IC's, its heavily used inside all kinds of devices, Originally invented to be used inside TV,s as a connection between the main controller, the remote control interface, the front touch buttons, the Teletext receiver the Real Time Clock, etc etc. Today is use has exploded in thousands of devices, making it possible that all kinds of subparts in a device can talk to each other. For example in a satellite its often used as the internal "bus" so that the main controller can talk with the "maximum power point tracker", the gyroscope, and the "star tracker". To mention just a few devices inside a sattelite.
SPI (serial peripheral interface) allows a single "master" (the R-PI) to "talk to" a number of "slave devices" (in case of the raspberry two, but the number can be expanded) at high speed. Its use is the fast transfer of lots of data, for example its the basic interface mode for SD-Cards (so it could be used to connect a second SD-cardslot to the R-PI). Its used for all kind of high speed connections (except for sound for which other specialized standards exists).
Although a bit hidden the R-PI also has a PWM (pulse width modulation) output, these can be used as simple analog to digital converters (but generally not for sound), But the most common use is for controlling servo motors.
GPIO pins can also be combined to create new kinds of interfaces, and the possibilities of those are endless.