This is quite a technical legal subject and I am not sure if I can explain it properly.
1. An in personam judgement would be a judgement passed by a court against the company, where the court actually has legal jurisdiction over the company. To explain, a person or a company may be found guilty in a country which has no jurisdiction over him, in which case they could not actually enforce that judgement. So let us say a Chinese court finds an American company guilty of industrial espionage or hacking. This could not be an in personam judgement as Chinese courts have no jurisdiction over American companies. In such cases an in rem judgement may be passed so that the Chinese courts can move against any Chinese property that the company may own. That, at least is my understanding of it.
2. So the statement you have given is saying that the BVI courts would accept any in personam judgements against the company in question (ie judgements passed against the company in any country where the courts actually have jurisdiction over the company). The bit in brackets makes some exceptions for cases such as unpaid taxes etc. (ie if there is a judgement against the company of unpaid taxes, this would not count in the BVI, presumably because tax demands can always be challenged).
I hope that makes some sense, but I should warn you that I am not a lawyer and you probably need a qualified lawyer to explain this properly. You will be a legal expert soon if you carry on like this!