Short answers, pulled from the story.
i18n stands for internationalization and l10n stands for localization. The abbreviations are numeronyms: 18 represents the letters between the first i and last n in internationalization, a convention coined at Digital Equipment Corporation in the 1970s or 1980s.
Internationalization is the engineering process of designing software so it can be adapted for different languages and regions without rebuilding the core; it is typically done once. Localization is the process of adapting that internationalized software for a specific language or region, including translating text and adding locale-specific components; it is repeated for each target market.
The Common Locale Data Repository, maintained by Unicode, collects standardized data about locale differences such as writing direction, number formatting, and sorting rules. It is used by major operating systems including Microsoft Windows, macOS, and Debian, and by internet projects such as Google and the Wikimedia Foundation.
In the early 1980s, Lotus 1-2-3 spent two years separating its program code from text strings, delaying its European localization. That delay cost it the market lead in Europe, which Microsoft Multiplan captured.
The GNOME project relies on volunteer translation teams covering over 100 languages. This decentralized model is possible because the software was properly internationalized first, allowing localization work to be distributed to community contributors.
The Microsoft Excel localization team translated formula tokens as a byproduct of localizing number and date formats, so that users with no English background could read spreadsheet formulas in their own language. The trade-off was that internet searches for formula help across different language versions returned incompatible results before machine translation of web pages became common.