In Japanese, the 連用形（れんようけい） (conjunctive form) is often called ‘the ます form’, or ‘the conjunctive form’. ‘The conjunctive form’ is much more accurate, as 連用形（れんようけい） is used with more than just verbs. Basically, the 連用形（れんようけい） is the form of any word that will be used in standard conjugation with other structures. For い-Adjectives, this is the form that uses く, for verbs, the ます stem.
The reason that 連用形（れんようけい） is sometimes referred to as ‘the formal conjunctive’ is due to its use before a comma. Usually, the 接続助詞（せつぞくじょし） て would be used to separate clauses in sentences, however, the formal conjunctive allows this to be done without て. Let’s look at some examples.

• 飛行機（ひこうき）のエンジンが爆発（ばくはつ）をし、海（うみ）に墜落（ついらく）した。
  The engine of the airplane exploded, (and) it crashed into the ocean.
• 朝食（ちょうしょく）を食（た）べ、出（で）かける準備（じゅんび）をしてください。
  Eat your breakfast, (and) please get ready to go out.
• 北海道（ほっかいどう）は寒（さむ）く、景色（けしき）が綺麗（きれい）。
  Hokkaido is cold, (and) the scenery is pretty.
• 学校（がっこう）は楽（たの）しく、色々（いろいろ）学（まな）べるので学校（がっこう）が好（す）きです。
  School is fun, (and) I can learn various things so I like it.

As we can see, although て is not required, a 読点（とうてん） (Japanese comma) will be required to prevent the sentence from becoming confusing.