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A local variable in Bash is a variable whose scope is restricted to the execution context of the function in which it is declared, including any child functions invoked within that call stack. Declaring a local variable shadows any globally scoped variable or outer-scoped local variable sharing the same identifier until the declaring function terminates.

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Syntax and Declaration

Local variables are instantiated using the local shell builtin. The local command is functionally equivalent to declare but is strictly limited to function scope. It accepts the same attribute flags as declare. 
function define_locals() {
    # Standard local declaration and assignment
    local var_name="string_value"
    
    # Local declaration with attribute flags
    local -i int_var=42       # Integer attribute
    local -r const_var="foo"  # Readonly attribute
    local -a array_var=(1 2)  # Indexed array attribute
    local -A dict_var         # Associative array attribute
}

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Technical Mechanics

Dynamic Scoping Unlike languages that utilize lexical (static) scoping, Bash employs dynamic scoping. A local variable is visible not only to the function that declares it but also to any subsequent functions called from within that function’s execution block. 
function parent_func() {
    local shared_var="parent_scope"
    child_func
}

function child_func() {
    # Inherits access to shared_var due to dynamic scoping
    # Modifying it here modifies the parent_func's local instance
    shared_var="modified_by_child"
}
Execution Context Restriction The local builtin is strictly bound to function execution. Attempting to invoke local in the global scope (outside of a function definition) results in a runtime error: bash: local: can only be used in a function. Shadowing and Call Frame Restoration When a local variable is declared, Bash allocates a new memory space for the identifier within the current call frame. Any existing variable with the same name in a higher scope is shadowed. Once the function returns, the local call frame is destroyed, and the shadowed variable’s original value and attributes are restored to the environment. Exit Code Masking A critical mechanical behavior of local occurs during command substitution. Because local is a builtin command, combining declaration and command substitution on a single line causes the exit status ($?) to reflect the success of the local assignment (which is 0), thereby masking the exit status of the substituted command. 
function masked_exit_code() {
    # The exit code of 'some_command' is masked. $? will evaluate to 0.
    local result=$(some_command)
    
    # Strict mechanical approach: Declare first, assign second.
    local result
    result=$(some_command) # $? will correctly reflect some_command's exit status
}
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