Indexing radical on the left - silk threads were used in antiquity to keep tallies, bind documents, and mark off intervals. 纟 puts 纪 in a recording/ordering family with 经 (classic), 续 (continue), 纲 (cardinal principles), and 纹 (pattern).
Right side supplies the sound (jǐ → jì, only the tone shifts). 己 originally pictured a knotted cord - fitting alongside the silk radical, since the whole character evokes tying off knots to mark a year, an era, or a record.