More than "an opportunity", it should read "will be forced to", as it will begin with no trade deals with other countries and will default to the WTO rules.
For the answerable part:
A country within the EU cannot sign its own, separated trade deals, because the single market would mean that once the goods are in that country they can travel everywhere in the EU. For example, if there is a 10% tariff in bananas and Spain signed a trade deal agreeing to a 0% tariff, everybody would import bananas to any country of the EU through Spain.
And getting the EU to sign a trade deal is not easy. The fact that the EU is formed by many countries mean that getting a trade agreement that is acceptable to all of them is considerably more difficult1.
The UK will have an advantage of being a more "coherent" market, which means some trade deals may be easier to reach. If there are no banana producers in the UK, there would be little opposition to a trade deal that eases the import of bananas in the country. This should lead to more agility for creating trade deals.
Of course, there is a downside to this: the UK will be a considerably smaller market than the EU. This means that the other part will benefit less from probable trade deals (selling their bananas to 65 million people instead of 430 million), so they may be less interested in making deals that help UK business to sell to them.
And the above leads to the fact that, as of now, we cannot predict if the situation will end as a net advantage for the UK or not; we cannot even predict if we will be able to tell that in the future (what if it helps industry but hurts financial services?)
That is already is an issue within a country (business that feel threatened by foreign competition opposing the trade deal, business that think that they can increase they market are in favor), with all of the countries of the EU it is considerably more complicated.