Sex-linked inheritance
The sex chromosomes carry ordinary genes as well as deciding sex. Because the X and the Y are not the same size, those genes do not behave the way genes on the autosomes do.
Sex-linked characteristics
Characteristics controlled by genes carried on the sex chromosomes are called sex-linked. In practice this nearly always means the X chromosome, because the much smaller Y carries very few genes.
One X against two
For a gene on the X chromosome, the two sexes are not in the same position at all.
A woman has two X chromosomes
So she has two alleles of every X-linked gene, exactly as for any autosomal gene. A recessive allele on one X can be masked by a dominant allele on the other.
A man has one X and one Y
So for most X-linked genes he has only one allele. There is no second copy on the Y to mask it, and whatever that single allele says is what shows.
Why that makes males more often affected
A woman shows a recessive X-linked condition only if she inherits the recessive allele twice — once from each parent. A man shows it if he inherits it once, from his mother. One event is far more likely than two, which is why conditions such as haemophilia and red-green colour blindness are seen much more often in men.
Dominant and recessive still mean the same thing
Nothing about dominance has changed. What has changed is that a male has no second allele for the dominant one to be dominant over. A single recessive allele shows in him not because it has become dominant, but because it is unopposed.
One copy is enough in a male
Genes on the X chromosome are sex-linked. A female has two alleles and can carry a recessive one hidden; a male has only one, so a single recessive allele shows in him.