Generally, the candidate solutions are encoded as bit strings.
Crossover provides a method of combining two candidates from the population to form a new candidate.
The most important part of a GA is the fitness function which gives an evaluation for each candidate as to how good a soultion it is. When candidates are chosen for crossover they are picked in proportion to their relative fitness to the entire population. There are many efficiency issues in the parallel implementation of GA's. See section 4 of this document for more ideas. The computation of relative fitness may require global communication so data layout becomes important.