The language they're using for that sounds like the language used for undergraduate admissions in the UK (via the UCAS system). We don't use that language for PhDs at my institution (that I'm aware of), but maybe it is part of a standard system elsewhere.
That terminology comes in two parts.
The first is the university's response to your application - this can be rejected, conditional, or unconditional. Rejected is straightforward, conditional means they accept you provided you meet some criteria (usually successful completion of a current course with a particular grade) and unconditional means they're happy to accept you without any further conditions.
The second part is your response. The two relevant options here are decline or firm. Decline is again straightforward, while firm means you've indicated that you want to accept the position. It's 'firm' rather than something like 'accept', because the undergraduate system also lets you specify second-preference ('insurance') courses, which you can take up if you don't get conditional grades for your first choice.
Details on the undergraduate decision system is available e.g. on the UCAS website.
So, if that was an undergraduate position, I'd interpret that as they've offered you the position without further conditions, and you've accepted it, so you're good to go.
However, as I mention above, this is not universally standard language for a PhD application, so I wholeheartedly endorse the suggestion in the comments to double-check with the university if you have any doubts!