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Verilog is a hardware descriptive language. It allows digital logic circuits to described in a high level language rather than in individual logic gates.
The syntax of Verilog is very similar to the C programming language which makes it easy to learn. Originally Verilog was a proprietary language rather than an open standard. VHDL has always been an open standard and thus used to be more common for hobbyists and begineers. VHDL and Verilog do essentially the same thing, they are just different languages.
Verilog is an HDL ( Hardware Description Language). It's used to describe digital logic circuits. After a Verilog code is written, it's simulated to assure functionality, and then it's synthesized to logic gates. These logic gates are then placed on an integrated circuit, operating and givng whatever function already described by the verilog code written earlier. That's the explanation in very simple terms