It is known as the Attribution gadget and generally found in the footer of the templates, but may be thrown anywhere in third-party templates. You cannot directly remove it because it is locked by default by blogger. It is very easy to remove it. Below is a small tutorial in removing "Powered by blogger" from your blog.
Remove Powered By Blogger From Your Blog
Step 1 : Open your blogger dashboard. Go to "Template" and then click on "Edit HTML".
Step 2 : Click anywhere inside the code. Now using the keys Control+F, open the search box as shown in the picture below.
Step 3 : Write the code given below in the search box and hit enter to search it.
</head>
Step 4 : Just above this code, copy and paste the following code given below
<style>
#Attribution1 {
display: none;
}
</style>
display: none;
}
</style>
Step 5 : Save the template and you are all done. You can see now there will be no annoying "powered by blogger" message.
I hope this tutorial helped you in removing this gadget.