Checkbox multiple and save in bank

To do this, you only have to assign indexes to these array, even in the HTML form.

<div class="info"><?php echo isset($msg) ? "<h2>Retorno:</h2>" . $msg . "<hr>" : NULL; ?></div>
        <h2>Formulário:</h2>
        <form method="POST" action="">
            <input type="text" name="nome" placeholder="Digite o seu nome"/><br/><br/>
            <h3>Trabalhou como:</h3>
            <label for="check[med]">Médico(a):
            <input type="checkbox" name="check[med]" value="Médico(a)"/>
            </label><br/>
            <label for="check[mec]"> Mecânico:
                <input type="checkbox" name="check[mec]" value="Mecânico(a)"/>
            </label><br/><br/>
            <input type="submit" name="enviar" value="Enviar"/>
        </form>

And with PHP you just read the values contained in them.

if(isset($_POST["enviar"])){
    $nome = isset($_POST["nome"]) ? (string) $_POST["nome"] : NULL;
    $prof = isset($_POST["check"]) ? $_POST["check"] : NULL;
    if(!empty($prof) && !empty($nome)){ 
        $msg = null;
        $msg .= "<b>Nome:</b> " . $nome . "<br/>";
        $msg .= "<b>Já trabalhou como: </b><br/>";  
        foreach($prof as $val){ 
            $msg .= $val . "<br/>";
        }   
    }   
}

This example is simple and easy to test. If you continue with some questions, make some changes to HTML and use print_r($_POST) to see what values have been sent, and how they are identified or organized in that array.

In this case, the use of BIT-to-BIT operators fall like a Glove. For this it is important to understand the concept.

An example code. Assuming I have 4 options that can be selected individually or simultaneously: student, employee, voter, disabled I assign to each one, power value of 2 starting at 0

estudante = 2^0 = 1
empregado = 2^1 = 2
eleitor = 2^2 = 4
deficiente = 2^3 = 8

To assign any one of them just add it to the total Eg: To assign employee, voter and disabled I am 2 + 4 + 8 = 14 When viewing the checked options I use the & (E Commercial or Ampersand) to know if the option is contained in the total

    2 & 14 == 2 // Se o resultado da operação for o próprio valor ele está contido
    1 & 14 == 1 // Nesse caso, como 1 não está contido no total, o resultado será 0

So, just adapt this rule to your need.

If you just want to retrieve an HTML information and save to the database use the same common form.

    <input type="checkbox" value="1" name="depilacao" />

In PHP it will recover by the NAME attribute

    $depilacao = isset($_REQUEST['depilacao']) ? (int) $_REQUEST['depilacao'] : null;
    // ...
    if ($depilacao > 0 ) // Marcou a opção depilação

Just clarifying the comment that said it would have many conditions using BIT operator to BIT: As I explained, you can have as many options as you want a simple code will solve by saving the sum in a single field in the database and have a table with only the services that you want to appear as an option. Having a column for each service is the wrong way to do it.