Prestashop is by default convert your logo image in png or gif format logo to jpg format.
This sometimes makes it difficult for you if you have a patterned page background and you want your logo to fit in without it having an ugly white border around your logo see example below:

Instead you want it to look like below:

To make this possible you have to edit your header.tpl
If you try to upload a png logo from back-office it will only be converted to jpg.
So first step is to open up your header.tpl file in your theme.
Find the code:
<a id=”header_logo” href=”{$base_dir}” title=”{$shop_name|escape:’htmlall’:'UTF-8′}”>
<img src=”{$img_ps_dir}logo.jpg?{$time}” alt=”{$shop_name|escape:’htmlall’:'UTF-8′}” {if $logo_image_width}width=”{$logo_image_width}”{/if} {if $logo_image_height}height=”{$logo_image_height}” {/if} />
</a>
Replace (marked red) jpg with png:
<a id=”header_logo” href=”{$base_dir}” title=”{$shop_name|escape:’htmlall’:'UTF-8′}”>
<img src=”{$img_ps_dir}logo.png?{$time}” alt=”{$shop_name|escape:’htmlall’:'UTF-8′}” {if $logo_image_width}width=”{$logo_image_width}”{/if} {if $logo_image_height}height=”{$logo_image_height}” {/if} />
</a>
Upload your new png logo in back-office.
If it doesn’t work you can upload it manually save it as logo.png in your prestashop root /img