Do you mean a travel agent or perhaps a tour operator?
A tour operator arranges the flights, accommodation, any trips etc into one package. A travel agent mainly sells packages on behalf of tour operators.
Some companies can be both a tour operator and a travel agent.
If you're buying a package holiday from a UK based tour operator then, if things go wrong while you're on holiday, they're on the hook to sort things out.
Personally, if we're just going somewhere quite normal, maybe a week in the Med or a fly/drive holiday in the States or Canada then we would typically book the flights and accommodation separately ourselves.
However, you can sometimes get better deals from an airline if you also book accommodation through them as well, so it's always worth checking that out as well.
Where I would definitely use a tour operator (and always have in the past) is when we are going somewhere a bit more distant and, especially, when it involves transport arrangements in countries with either less developed infrastructure or a language we would struggle to understand.
For example, over the decades we have been to China, a couple of Central Asian countries, a couple of African countries and a South American country.
Each of these holidays involved quite a bit of transport in-country between different locations and we really appreciated the fact that this had all been sorted out for us.
Tour operators are also very useful for help with getting appropriate visas as well.
So, if it's just lying on a beach then I'll book it directly myself, if it involves a lot of logistics in the country that we're going to then I'll happily leave making the arrangements to the tour operator.
Although, even then, I'll sometimes book the flights separately and have a "land only" price where the tour operator arranges everything apart from the flights to/from the UK.