Export your profile on the old computer. https://support.mozilla.org/kb/thunderbird-export

Import your profile on the new computer. https://support.mozilla.org/kb/thunderbird-import

Export/Import isn't very convenient for this. In addition to that requiring a special procedure if the size of the profile folder is greater than 2 GB, importing your profile on the new computer would require Thunderbird to be already running there to begin with, and then Thunderbird won't even let you import a profile without setting up a mail account first…

The following article describes a better way to do it:

https://support.mozilla.org/kb/moving-thunderbird-data-to-a-new-computer

Well, for the record, before posting my previous reply I tried to run Thunderbird without setting up a mail account, and the Tools > Import command was disabled, hence what I said. But I tried again now (while checking something else), and this time the Import command was enabled, so contrary to what I said, it looks like it is (or should be) possible to import an existing profile (no greater than 2 GB) that way without having to set up a mail account first.