A module
is a block of Verilog code that implements a certain functionality. Modules can be embedded within other modules and a higher level module can communicate with its lower level modules using their input and output ports.
Syntax
A module should be enclosed within module
and endmodule
keywords. Name of the module should be given right after the module
keyword and an optional list of ports may be declared as well. Note that ports declared in the list of port declarations cannot be redeclared within the body of the module.
module <name> ([port_list]);
// Contents of the module
endmodule
// A module can have an empty portlist
module name;
// Contents of the module
endmodule
All variable declarations, dataflow statements, functions or tasks and lower module instances if any, must be defined within the module
and endmodule
keywords. There can be multiple modules with different names in the same file and can be defined in any order.
Example

The module dff represents a D flip flop which has three input ports d , clk , rstn and one output port q . Contents of the module describe how a D flip flop should behave for different combinations of inputs. Here, input d is always assigned to output q at positive edge of clock if rstn is high because it is an active low reset.
// Module called "dff" has 3 inputs and 1 output port
module dff ( input d,
input clk,
input rstn,
output reg q);
// Contents of the module
always @ (posedge clk) begin
if (!rstn)
q <= 0;
else
q <= d;
end
endmodule
Hardware Schematic
This module will be converted into the following digital circuit during synthesis.

Note that you cannot have any code written outside a module !
What is the purpose of a module ?
A module represents a design unit that implements certain behavioral characteristics and will get converted into a digital circuit during synthesis. Any combination of inputs can be given to the module and it will provide a corresponding output. This allows the same module to be reused to form bigger modules that implement more complex hardware.
For example, the DFF shown above can be chained to form a shift register.
module shift_reg ( input d,
input clk,
input rstn,
output q);
wire [2:0] q_net;
dff u0 (.d(d), .clk(clk), .rstn(rstn), .q(q_net[0]));
dff u1 (.d(q_net[0]), .clk(clk), .rstn(rstn), .q(q_net[1]));
dff u2 (.d(q_net[1]), .clk(clk), .rstn(rstn), .q(q_net[2]));
dff u3 (.d(q_net[2]), .clk(clk), .rstn(rstn), .q(q));
endmodule
Hardware Schematic
Note that the dff instances are connected together with wires as described by the Verilog RTL module.

Instead of building up from smaller blocks to form bigger design blocks, the reverse can also be done. Consider the breakdown of a simple GPU engine into smaller components such that each can be represented as a module that implements a specific feature. The GPU engine shown below can be divided into five different sub-blocks where each perform a specific functionality. The bus interface unit gets data from outside into the design, which gets processed by another unit to extract instructions. Other units down the line process data provided by previous unit.

Each sub-block can be represented as a module
with a certain set of input and output signals for communication with other modules and each sub-block can be further divided into more finer blocks as required.
What are top-level modules ?
A top-level module is one which contains all other modules. A top-level module is not instantiated within any other module.
For example, design modules are normally instantiated within top level testbench modules so that simulation can be run by providing input stimulus. But, the testbench is not instantiated within any other module because it is a block that encapsulates everything else and hence is the top-level module.
Design Top Level
The design code shown below has a top-level module called design. This is because it contains all other sub-modules requried to make the design complete. The submodules can have more nested sub-modules like mod3 inside mod1 and mod4 inside mod2. Anyhow, all these are included into the top level module when mod1 and mod2 are instantiated. So this makes the design complete and is the top-level module for the design.
//---------------------------------
// Design code
//---------------------------------
module mod3 ( [port_list] );
reg c;
// Design code
endmodule
module mod4 ( [port_list] );
wire a;
// Design code
endmodule
module mod1 ( [port_list] ); // This module called "mod1" contains two instances
wire y;
mod3 mod_inst1 ( ... ); // First instance is of module called "mod3" with name "mod_inst1"
mod3 mod_inst2 ( ... ); // Second instance is also of module "mod3" with name "mod_inst2"
endmodule
module mod2 ( [port_list] ); // This module called "mod2" contains two instances
mod4 mod_inst1 ( ... ); // First instance is of module called "mod4" with name "mod_inst1"
mod4 mod_inst2 ( ... ); // Second instance is also of module "mod4" with name "mod_inst2"
endmodule
// Top-level module
module design ( [port_list]); // From design perspective, this is the top-level module
wire _net;
mod1 mod_inst1 ( ... ); // since it contains all other modules and sub-modules
mod2 mod_inst2 ( ... );
endmodule
Testbench Top Level
The testbench module contains stimulus to check functionality of the design and is primarily used for functional verification using simulation tools. Hence the design is instantiated and called d0 inside the testbench module. From a simulator perspective, testbench is the top level module.
//-----------------------------------------------------------
// Testbench code
// From simulation perspective, this is the top-level module
// because 'design' is instantiated within this module
//-----------------------------------------------------------
module testbench;
design d0 ( [port_list_connections] );
// Rest of the testbench code
endmodule
Hierarchical Names
A hierarchical structure is formed when modules can be instantiated inside one another, and hence the top level module is called the root. Since each lower module instantiations within a given module is required to have different identifier names, there will not be any ambiguity in accessing signals. A hierarchical name is constructed by a list of these identifiers separated by dots .
for each level of the hierarchy. Any signal can be accessed within any module using the hierarchical path to that particular signal.
// Take the example shown above in top level modules
design.mod_inst1 // Access to module instance mod_inst1
design.mod_inst1.y // Access signal "y" inside mod_inst1
design.mod_inst2.mod_inst2.a // Access signal "a" within mod4 module
testbench.d0._net; // Top level signal _net within design module accessed from testbench