I really want to study Law at university and then probably become a lawyer after. However I recently heard a Rabbi say that one has to be careful in studying/practising secular law so as not to break any Jewish laws. Could you explain what this means in practise?

In practice, there is a problem if you know that according to the halacha your client owes money to the person suing him, but according to the secular law he is not obligated to pay him. You would not be allowed to work to free him of his obligation to pay. The problem exists also in the exact opposite case: your client is suing someone for money to which he is not entitled according to halacha. Criminal proceedings present less of a halachic problem as does dealing with laws based not on legal principles contrary to halacha (e.g. German law, Turkish law, English law), but rather to regulate commerce etc. There are lawyers who are seriously Torah observant and they are able to examine each case and to decide what to do on a case to case basis.