What is sperm, egg, zygote, embryo, and larva?

Sperm is the male gamete, or sex cell, and contains the male's genes.  The egg is the female organism's gamete, and contains the female organism's genes.  When a sperm cell and an egg cell combine, the resulting cell is called an embryo, or fertilized egg. This process occurs in all sexually reproducing organisms, including both plants and many animals.  A larva is the juvenile life stage in certain animals, such as many insects, amphibians, etc.  For example, a tadpole is a frog's larval stage; a caterpillar is a butterfly's larval stage; a maggot is a fly's larval stage, etc.  This life stage occurs before the animal metamorphoses into an adult.

Freak gave a pretty good answer, but left out a definition of the term "zygote".  When a sperm and an egg unite they form a zygote: a fertilized egg.   An embryo can have hundreds of cells, but a zygote can only have the 1.