What do the letters and numbers in a haplogroup name mean, like H1a1?

The opening letter is the major branch (here, H), and each added character marks a deeper, more recent split down that branch: H → H1 → H1a → H1a1. A longer name simply means a finer, younger twig of the same limb — not a different lineage. How deep a name we can give you depends on how many mitochondrial positions your file covers.