Learn Romanian: Pun apa la fiert. - I'm putting the water on to boil.

This is the Romanian supine mood. It looks exactly like the past participle, but it acts like a noun describing an action. When stating the purpose of an object, Romanian uses a preposition like la (at/to) followed by the supine. So la fiert translates closer to "for boiling".

Could I use the subjunctive and say Pun apa să fiarbă?

Yes! Pun apa să fiarbă (literally "I put the water so that it boils") is a perfectly natural alternative. Using la plus the supine just acts as a slightly more compact, fixed phrase for common household tasks.

Why is the word for water apa rather than apă?

Since you are talking about specific water (the water you intend to boil), it needs the definite article "the". For feminine nouns ending in -ă, you replace the -ă with -a, turning apă into apa.

Why isn't there a word for "on" like in the English translation?

In English, "putting on" is a phrasal verb specific to things like stoves or fires. Romanian simply uses the base verb a pune (to put) alongside the purpose la fiert. Trying to literally translate "on" would sound unnatural here.