In English, the word "awkward" can be used to describe a situation that is uncomfortable and embarrassing (but neither word seems to fully describe what "awkward" describes). What is the best translation of this concept in Spanish? If a single word doesn't fully capture the English meaning, what phrase would best describe it?
Actually, I don't think we have such a precise word as 'awkward' (I've missed it).
As per other answer, "incómodo" is the most commonly used word. But because "incómodo" means in general "uncomfortable", this sense is often made more explicit: "Una situación incómoda", "Un momento incómodo", etc.
Other words are "(momento) embarazoso" (more precise, but less colloquial), or "violento" (which also is ambiguous).
In addition to incómodo which has already been suggested, Linguee.com (which I suggest you take a look at) also suggests
delicado, extraño, dificil
when describing a situation (as opposed to a person). Which is what you appear to be asking about.
You can help us help you by including a sample context.
Other two possibilities: