Learn German: Er trinkt beim Training Wasser. - He drinks water during practice.

beim is a contraction of the preposition bei and the dative article dem. The preposition bei always forces the following noun into the dative case. Since Training is a neuter noun (das Training), its article changes to dem. Instead of saying bei dem, German speakers almost always shorten it to beim.

I thought bei meant "at" or "with". Why is it translated as "during" here?

You are right that bei is often used for locations or people (like being "at" someone's house). However, when you use bei with a noun that describes an event or an activity, like das Training (practice) or das Essen (the meal), it takes on a temporal meaning. In these cases, it translates to "during" or "at the time of" that activity.

Why is the order "beim Training Wasser" instead of "Wasser beim Training" like in English?

In German, there is a general rule for sentence structure: expressions of time usually come before the direct object. Because beim Training tells us when he is drinking, it naturally comes before Wasser, which is the direct object telling us what he is drinking.

Is Training just the English word? Why does it act like a German noun?