Here's the mating cycle of yeast taken right out of my lecture slides:
Diploid: Having full the full set of chromosomes (one from mother, one from father; or two copies of homologous chromosomes)
Haploid: Having half the full set of chromosome (half the diploid; or one copy of a homologous pair)
Budding: Asexual reproduction by creating a mini-clone of the self that 'buds' off to create a new cell with the exact same genetic make up
Spore: The 4 haploid cells that are released when the yeast chooses to go with sexual reproduction
In yeast, the two haploid spore types that are formed during sexual reproduction are called an a cell or an a cell. You can kind of think of these cells as akin to male and female. These haploid cells are able to reproduce their haploid genome via budding.
Mating occurs when one a cell finds another a cell and the two halves of a full diploid combine together, fusing their membranes and joining their DNA into one. I think the notion that in order to become a full diploid yeast cell, two haploids have to find each other and literally fuse into one, is really quite romantic.
To top that off, if a haploid cell has a loss of function mutation in a gene (let's call it gene A), it's overall growth and survival is very limited since they don't have a correct copy of said gene to make up for the one mutation. Now say there's another haploid with a mutation in a different gene (let's call it gene B) but has a functional copy of gene A. If these two haploids mate then they will fuse their genes together so that there are now two copies of each gene. Since one haploid had the wildtype (functional) allele for gene A and the other haploid had the wildtype allele for gene B, the diploid cell will have two perfectly functional alleles for both gene A and gene B! The two haploids complement each other's flaws so perfectly!
Of course, in the case that both haploids have a mutation in the same gene, well, their resulting relationship will also be pretty in-viable... I guess it's all about finding the right match.