てからというもの is an extension of the grammar point てから meaning 'after (A)', and partners と言（い）う 'that which is' with もの 'thing'. It is often translated as 'ever since (A)', and will always express a new state of (B) that has been ongoing since (A). Although the literal translation is 'with that which was from (A)', the fact that (B) is ongoing is simply implied.
As with てから, this structure will be seen following verbs in their て-form.

• この会社（かいしゃ）に入社（にゅうしゃ）してからというもの、日付（ひづけ）が変（か）わる前（まえ）に家（いえ）に帰（かえ）ったことがない。
  Ever since I joined this company, I have not been home before the clock ticks over midnight.
• 仕事（しごと）に行（い）く前（まえ）に散歩（さんぽ）に行（い）くようにしてからというもの、どんどん体重（たいじゅう）が減（へ）ってきたのでこれからも散歩（さんぽ）を続（つづ）けようと思（おも）っている。
  Ever since I started to go on walks before work, I have been steadily losing weight, so I am thinking of continuing to go on walks.
• ファイナルデスティネーションという映画（えいが）を見（み）てからというもの、木材（もくざい）を運（はこ）んだトラックの後（うし）ろを走（はし）るのを避（さ）けるようになった。
  Ever since watching the movie 'Final Destination', I have been avoiding driving behind trucks carrying lumber.

Although not quite as common, からというもの may be seen following それ, when それ is at the beginning of a new sentence. In these cases, それ will linked to what was stated in the previous sentence.

• 彼（かれ）は社長（しゃちょう）にみんなの前（まえ）でものすごく怒（おこ）られた。それからというもの彼（かれ）は別人（べつじん）になったかのように性格（せいかく）が変（か）わった。
  He was yelled at in front of everyone by the boss. Ever since that event, he became a different person.
• 先月（せんげつ）彼女（かのじょ）が痴漢（ちかん）にあった。それからというもの、満員（まんいん）電車（でんしゃ）を避（さ）けるようになった。
  She was groped last month. Ever since then, she has been avoiding packed trains.