Answer:
The expression of a recessive trait occurs when two recessive alleles recombine.
I'm going to use an example for this. Let's say that blue hair is recessive, and black hair is dominant.
B = Black hair
b = Blue hair
If you have the parents:
Parent 1: Bb (Has black hair; it dominates blue hair... but is a carrier of the blue hair gene.)
Parent 2: bb (Has blue hair; only recessive genes are present)
If you use a punnet square,
They have four possible combinations of kids:
Kid 1: Bb (Black haired; is a carrier of blue hair)
Kid 2: Bb (Black haired; is a carrier)
Kid 3: Bb (Black haired; is a carrier)
Kid 4: bb (Blue haired)
These "carriers" are able to have a chance of producing a child with the same recessive gene, whether it be displayed or just carried.
It's very confusing, but simple once you get the hang of it. :3