Learn Portuguese (Portugal): O nutricionista mandou que eu bebesse mais água. - The nutritionist ordered that I drink more water.

Because this is reported speech reporting a command. The nutritionist originally gave an imperative command (like Beba mais água!). When we report a command after a past tense verb like mandou, that command shifts into the imperfect subjunctive (bebesse).

How is the form bebesse built?

The imperfect subjunctive is always built from the eles form of the simple past. For beber, that form is beberam. You drop the -ram and add the imperfect subjunctive ending. For eu, that ending is -sse, making bebesse.

Why is it O nutricionista when the word ends in an a?

Words ending in -ista (like nutricionista, dentista, or artista) are gender-neutral in their spelling. The article before the word tells you the gender. Since it is O nutricionista, we know we are talking about a male nutritionist. For a female, it would be A nutricionista.

Could I use the infinitive here and say mandou-me beber instead?