Similar to the Next Generation episode "The Enemy" (and the non-Star Trek movie Enemy Mine), the basic story of "Dawn" is being stuck with someone you really don't want to, and having to survive something other than each other.
This time around it's Trip who gets to enjoy the experience. Like "Precious Cargo" he gets to enjoy some quality time with an alien with the Universal Translator unavailable to help them communicate with each other. Unlike "Precious Cargo," that lasts throughout the episode, y'know, just in case things weren't already complicated enough.
I remember when the episode originally aired that a lot of what I was thinking was that "Dawn" was another Trip episode, that there was a definite different tone to the second season than the first. In the first season a Trip episode would have meant him sharing his experiences with someone else. Even in "Unexpected" only half the episode was spent on the alien ship where he got impregnated (if you have no idea what I'm talking about, you may need to see the episode to really understand what I'm talking about). Somehow both "Cargo" and "Dawn" leave him on his own to deal with a tricky alien contact situation.
(Of course, he makes that his own problem in the later "Cogenitor.")
It's not hard to see this one-two punch as a large part of the reason Trip started to really stand out for me. It's rare for a character to end up on their own in Star Trek, and even more rare for it to happen several times in a single season. (I'm not talking about Quark in Deep Space Nine, mind you. He normally existed in his own bubble, hence the infamous Ferengi episodes.) It was an indication to me that the creators of Enterprise had themselves marked Trip out as an unusually strong character, someone they could write into any scenario and need few crutches to support him. And he really was that strong.
I wouldn't go so far as to say you absolutely need to watch this particular episode to understand his appeal, but you wouldn't go wrong to enjoy it.
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Memory Alpha summary.