每个 JOIN 应该有相应的 ON 条款：

SELECT tbart.articles_id
FROM articles tbart LEFT JOIN
     articles_keyword tbjoin 
     ON tbart.articles_id = tbjoin.articles_id LEFT JOIN
     keywords tbkey 
     ON tbkey.id = tbjoin.keywords_id
WHERE tbkey.keyword = 'ipsum' ;

你的版本有两个 JOIN s和1 ON ，因此出现错误。

您没有使用 ON 每次联接后的子句：

SELECT tbart.articles_id 
FROM articles AS tbart
INNER JOIN articles_keyword AS tbjoin ON tbart.articles_id = tbjoin.articles_id 
INNER JOIN keywords AS tbkey ON tbkey.id = tbjoin.keywords_id
WHERE tbkey.keyword = 'ipsum'

我还将连接更改为 INNER 加入是因为 WHERE 子句只返回匹配的行。
如果你想保留 LEFT 联接并返回 articles 必须将此条件移到 ON 条款：

SELECT tbart.articles_id 
FROM articles AS tbart
LEFT JOIN articles_keyword AS tbjoin ON tbart.articles_id = tbjoin.articles_id 
LEFT JOIN keywords AS tbkey ON tbkey.id = tbjoin.keywords_id AND tbkey.keyword = 'ipsum'