Does (or can) Mozilla Thunderbird download email to your computer and off the server?

Does (or can) Mozilla Thunderbird download email to your computer and off the server?

I have a client, who wants to use Thunderbird for his email client. His email is building up on his hosting server and taking up space, so he needs to start downloading his email. I was wondering if Thunderbird does that (like Outlook) or does it check webmail and leave the email on the server?

Thanks.