DNA sequencing is the process of determining the order of the letters along a piece of DNA. The molecule itself is a physical object, but the result of sequencing is not a molecule — it is a written record of letters, something like "A T G C C A T G ..." continuing for as long as the piece being read.
Because there are only four letters — A, T, G, and C — the record is easy to store digitally. Each letter can simply be kept as a character in a text file, or encoded as a short pattern of bits. The mapping is arbitrary but consistent: for example, A could be 00, T could be 01, G could be 10, and C could be 11. Two bits are enough for four possibilities, so every letter of DNA costs only two bits of storage. The important point is not which code is chosen, but that a molecule has become a string of symbols a computer can copy, search, and compare.
Once DNA is a string, ordinary computing applies to it. A computer can count how often a letter appears, find a short pattern inside a long sequence, or line up two sequences side by side. None of that requires understanding biology; it requires only that the biological information has been turned into characters.