The terminal sire is the one used to produce the prime meat lambs.
Sheep production in the UK is stratified; hill, upland and lowground. Hill ewes will go to hill tups to produce pure bred replacements and store lambs that will be fattened on good lowland pasture. Older hill hill ewes will come off the hard hill on to upland pasture and go to a crossing sire like Blue faced Leicester, Border Leicester to produce Mule and half bred lambs; the males are sold as stores to lowground farms and fattened for meat and ewe lambs go into the lowground flocks. These mules and halfbreds have the hardiness, thriftiness and good mothering of the hill breeds and the prolificacy and milkiness of the crossing breed; the mules / halfbreds are on good lowland pasture and crossed to the terminal sires from meat breeds - Suffolk, Beltex, Texel for example - to produce prime lamb at about 5 / 6 months.
This is a bit of an over simplification, but it gives you the idea.