A Microcontroller is a single chip computer. It's core is a CPU, around which there is RAM, ROM (Read only memory) (for program and constant data) and typically I/O units (Peripherals). Most microcontrollers also come with built-in oscillators in order to reduce the number of external components needed.
Most of today's microcontrollers are built around a 8/16 or 32-bit CPU core. However, there are also microcontrollers with multiple CPUs.
RAM stands for Random Access Memory.
ROM is non-volatile, read only memory. In most cases, it is actually Flash memory, which is a reprogrammable solid state memory.
An oscillator is a device that, given a certain frequency and constant voltage, can be used as a clock.
A Peripheral is a hardware device other than the processor and the memory. Peripherals can be basic digital I/O (also referred to as GPIO, general purpose I/O), or more complex things such as Timers, UART, SPI, Ethernet or CAN interfaces.