What is mean by the term "an organism's genotype is its specific combination of alleles for a given gene"?
From wikipedia


  An Allele is a variant form of a given gene.


Let's consider a simplified example. There is a gene for eye color and there are different alleles at this gene. The allele for blue eye, the allele for brown eye etc...

In a diploid (see ploidy) individual (humans are diploid), we have two copies of each gene (exception of sex chromosomes). Let's imagine, at a givne gene, there are 3 possible alleles called A, B and C. The possible combinations are 

AA
AB
AC
BB
BC
CC


The genotype of an individual for a given gene (I should say locus for the sake of generality) is called the genotype of an individual.


  Is it talking about heterozygous and homozygous[?]


The terms "homozygous" or "heterozygous" are adjectives to define whether, in a diploid genotype, the same allele is found on both haplotypes or not. In the above examples, 3 genotypes are homozygous (AA, BB and CC) and 3 genotypes are heterozygous (AB,AC and BC).


  [I]s it talking about the nuclear bases?


For two alleles to be different, they must differ in their sequence of nuclear bases of course.