to expand a little on Somchaya's answer,
you would use an interupt when a task on a microcontroller is time critical.
when an interupt is triggered the current program pauses and jumps to a different section of code (called the Interupt Service Routine or ISR on PICs).
when the interupt is over the program returns to where it left off in the main section of the program.
interupts are important when you need something to happen quickly.
as an example, imagine you had a complicated program that took a few seconds to complete each loop.
now imagine that you had a keyboard attached. you don't want to wait for a full iteration of the main program before the system responds every time a user types a key.
you would attach the keyboard to an interupt so user input was captured immediately.
Somchaya's encoder example is just a high speed version of the same problem. the interupt is needed to get timing information as accurate as possible.
SCL and SDA are the 2 lines on an i2c bus which is a 2 wire serial communication protocol commonly used for passing information between electronic components.
i use i2c whenever i have more than one microcontroller in a project. it's a very usefull way to pass information without much hardware.
i'm guessing LSDA and LSCL are a 2nd i2c channel.
what does the datasheet say?
the serial link that uses TX and RX can be connected to a PC serial port with a few extra components allowing you to control/read data from your project.
PWM (Pulse Width Modulation) is commonly used for controlling the amount of power going to something.
imagine you want to controll how bright an LED is. attach it to a PWM port. if you want it at 50% brightness, switch the pin it is attached to on and off so it is only on 50% of the time.
this is used a lot in DC motor controll.
to find out if a port is analog or digital, read the datasheet for the microcontroller on the board.
some pins can do either, depending on how you configure them.