The human genome is ~3 billion bases long (haploid), so even looking at that 1%, that's still millions of possible variations. Only close family members will have significant overlap.
What 23andMe measures are single nucleotide polymorphisms (SNPs). These are variations that are known to occur within the general population. For each of these positions, they can tell if you are homozygous (2 copies with the same ACGT), or heterozygous (One copy A, and another T, for example). Once you take all of that SNP data, you can get a good estimate of how closely related you are to another person. If you share the same patterns, you're likely related.
50% similarity would only be possible between a parent and a child. 25% would be likely between half siblings.