A combi boiler, or combination boiler, simply put makes hot water and heats your radiators up in one unit. There is no need for an additional hot water cylinder with a cold fill cistern or a header tank for the central heating system. They can be identified easily by the amount of pipes, they have typically 6-7.
Since 2005 all new boilers have, by law, had to be condensing. After that date there was a criteria that still allowed none-condensing boilers to be fitted, although very few were as the flexibility of new boilers meant that they could be fitted almost anywhere.