The processor, also known as the CPU (Central Processing Unit), is the primary component of a computer that performs most of the processing inside the computer.

Its key components include the Arithmetic Logic Unit (ALU), Control Unit (CU), and memory (registers). The ALU performs computations, the CU controls the operations of the CPU, and the registers store data.

The ALU is responsible for carrying out arithmetic and logical operations such as addition and subtraction, as well as comparison operations such as whether one value is equal to, greater than, or less than another.

The CU contains the decoder unit which interprets machine code instructions and controls the execution of them.

Understanding the fetch-decode-execute cycle is crucial. It's the process that the CPU uses to process an instruction: fetch the instruction from the memory, decode it, and then execute it.

There are different types of registers within the CPU: the Program Counter (PC), the Memory Address Register (MAR), the Memory Data Register (MDR), and the Current Instruction Register (CIR). Each has a specific function, ranging from holding memory addresses to be accessed, to storing the instruction currently being executed.

Cache memory is an important concept as well. This is a small amount of high-speed RAM on the processor that stores frequently used data, preventing the CPU from needing to fetch this data from the slower main memory.

Pipelining is the method in which the processor begins to process a second instruction before the first one has completed. This increases the throughput of the system.

The clock speed of the CPU, measured in Hertz, determines how many instructions a single core can process in one second. A higher clock speed indicates more instructions can be executed per second.

Multi-core systems, parallel execution, and concurrency are important concepts to understand. They refer to the abilities of a CPU to process multiple tasks at the same time, either by splitting tasks between cores, instruction level parallelism or simultaneous multi-threading.

Various factors can affect performance such as instruction set, data types, processor clock speed, dual-core / quad-core processors, cache memory and pipelining. Understanding the trade-offs associated with these factors is key.