Witness (to a crime), as a legal/technical term, is 目撃 in Japanese. Now why is this? It doesn't seem to relate well with any of the other possible translations for witness, such as 証人、見送る、 or 見届ける. A quick search did not turn up any results.
目 means 目で, with eyes.
The kanji 撃 sometimes means to hit, to touch, or to reach without hindrance, which is etymologically similar to the 届ける part in 見届ける, つける part in 見つける, etc. But the original meaning is not preserved in compound verbs any more.
大辞泉 gives a different explanation,
［常用漢字］ ［音］ゲキ（慣） ［訓］うつ １ 強くうち当てる。「撃柝(げきたく)／射撃・衝撃・打撃・鼓腹撃壌」 ２ 武力を加える。攻める。「撃退／迎撃・攻撃・襲撃・出撃・進撃・突撃・排撃・反撃」 ３ 感覚に触れる。「目撃」
But ３ is not very convincing to me. 強く(うち)当てる is better.