Definition
Information, in the technical sense due to Claude Shannon (1948), is the reduction of uncertainty produced by receiving a message. A message that resolves more uncertainty carries more bits of information. Hofstadter's GEB Topic 6 extends the notion: a message has three layers (frame, outer decoder, inner content), and "meaningful information" is what a sufficiently capable receiver can recover from the message's structure.
Why it matters
How it works
Shannon's information content of a message with probability p is -log₂(p) bits. A uniformly random binary digit carries 1 bit; an English letter, given the language's redundancy, carries about 1.3 bits despite there being 26 possibilities. To extract information, you need the codebook (Shannon's outer layer) — Hofstadter argues that for structured messages, the codebook is in principle reconstructible from the message itself.