The Arduino is a lot more basic than the Raspberry pie and personally find it a great way of learning electronics as there's no OS to worry about - Just write some code, click compile/upload and watch the board do its magic, much like typing and running some BASIC code on an old 8-bit home computer.
The main difference here is that the Arduino manipulates a series of I/O pins (digital, analogue and PWM), e.g. apply 5V, which can be linked up to relays, sensors, switches, electronic circuitry (e.g. LCD/OLED display) and so on.
It has 32KB of flash, 2KB of SRAM and 1KB of EEPROM, so definitely not something for a full blown OS.
A good example of a use would be a home-made data logger, e.g. for monitoring temperature, humidity, lux levels, motion, etc. with suitable sensors attached. Another example would be a home-made Christmas light controller, e.g. if you would like the lights to flash a certain sequence or respond to sound (like a disco light), etc.