One byte is 8 bits. The eight looks obvious now, but it was not inevitable — machines with 6, 7, 9 and 12-bit bytes were all built and sold, and the eight-bit byte won because of a specific design decision at IBM in the 1960s.
About the units
A bit is a single binary digit, the smallest unit of information: one of two states. A byte is the smallest individually addressable block of memory, and its size was a machine design choice rather than a law of nature. Early computers used six-bit characters, which allowed 64 distinct symbols — enough for uppercase letters, digits and punctuation, but not for lowercase. The IBM System/360, announced in 1964, adopted eight bits so that its character encoding could cover both cases plus control codes, and its commercial dominance made eight the standard everywhere. The term octet is used in networking standards precisely because it means eight bits unambiguously, without relying on the byte's history.
The exact factor
The factor is exactly 8, and both directions are exact. The consequence that matters daily is the difference between storage units and transmission units: storage is measured in bytes and network speed in bits per second. A 100 Mbit/s connection therefore transfers at most 12.5 MB/s, and a file of 1 GB takes at least 80 seconds on it. The convention is not arbitrary — serial links genuinely move bits, and framing overhead means the real throughput is lower still.
Where you meet this conversion
Anywhere storage meets transmission. Broadband advertising is the most familiar case, and the eight-fold difference between the advertised megabits and the observed megabytes in a download manager is the single most common source of complaints to internet providers. Video bitrates, audio encoding rates and memory bus widths are all quoted in bits, while the resulting files are measured in bytes. Cryptographic key lengths are always in bits: a 256-bit key is 32 bytes.