Is there a reason why specifically the word búho is written with an accent? Is there an orthographic rule that determines it? While I am used to accent marks above e I was quite surprised to see the u accented. Can any vowel be accented?
To split the diphthong "uo", otherwise it would be pronounced [bwo], with the stress in the "o".
Se tilda para romper el diptongo /uo/: si no se tildara sería una palabra monosílaba /buó/; gracias a la tilde es bisílaba /bú-o/.
Yes, there are specific rules about accents, and all vowels can be accented, it's not about the vowel, but about the stress. In this question you can read an introduction about accentuation in Spanish.
Any vowel (á, é, í, ó, ú) can have an accent mark placed over it, but it must follow the rules.
A Spanish learner must learn about how to properly divide words into syllables, understand the concept of a diphthong and a hiatus, know the weak vowels and strong vowels, and how to actually pronounce the words in question in order to properly add accent marks in the right place. Lastly, the learner should memorize the following rules.
There are rules for predictable pronunciation of written words in Spanish:
1) If a word ends in the letters n, s, or a vowel (a,e,i,o,u), it is pronounced stressing the second-to-the-last syllable or penultimate syllable.
Ex: ta/co, pe/rro, co/che, es/bel/to, com/pu/ta/dor/a— all of these words are pronounced with the audible stress on the penultimate or second-to-the-last syllable.
2) If a word ends in any other letter (b, c, d, f, g, h, j, k, l, m, p, q, r, t, v, w, x, y, z) [The bold letters are the most common ones], it is pronounced stressing the last syllable or ultimate syllable.
Ex: Hab/lar, au/daz, vi/rrey, ta/mal, cui/dad, re/loj, Na/ya/rit, al/co/hol—all of these words are pronounced with the audible stress on the ultimate or last syllable.
3) If the actual pronunciation of a word does not follow rules 1 and 2 like it should, a written accent mark is placed above the vowel in the syllable where the stress is heard (like a punishment, a scarlet letter).
Ex: árbol, hablé, comí, inglés, alemán, carbón, oír, freír— none of the words follow the rules.
NOTE: all words that have an audible stress in the third-to-the-last syllable or antepenultimate syllable, or beyond that point, will receive an accent mark above the vowel in the syllable in which the stress is heard
Ex: có/mi/co, ma/te/má/ti/cas, Que/ré/ta/ro, lin/güís/ti/ca, fe/nó/me/no— all of these words have accent marks because of the stress being in third-to-the-last syllable.
WEAK VOWELS: i, u
STRONG VOWELS: a, e, o
When we combine two weak vowels, or a weak vowel with a strong vowel, we get a diphthong which is an inseparable sound
Ex: iu, ui, ai, au, ei, eu, oi, ou, ia, ie, io, ua, ue, uo **—HEY! just like in the word búho!!! (the stress will be heard in the strong vowel of the diphthong)
When we combine two strong vowels, the two sounds separate into just that, two separate sounds or a hiatus.
Ex: aa, ae, ao, ea, ee, eo, oa, oe, oo —these are all two separate sounds.
So now, let's take a look at the words alcohol and búho, which both have a silent "h" between the vowels.
The word alcohol ends in an l, so the stress is on the last syllable, it follows the rules, so it doesn't get an accent mark. (Also in the word we hear the oo hiatus sound as though the h weren't even there).
The word búho ends in an o, so the stress should fall on the second to the last syllable, (it appears to follow the rules because the silent h tricks us.) but we must take into account the tricky silent h and the diphthong created by the uo next to one another.
Now let's analyze the diphthong "uo" as though the "h" were missing, because it essentially is. The u is weak, and the o is strong. So which one would be hear the stress on? ––On the "o".
So "buho" or "buo" by itself, without an accent mark, is pronounced like /buó/, whereas we know it should be /búo/, and that is why búho has an accent mark above the "u".
The following article from la Real Academia Española is very helpful for learning accent rules: Tilde.
I agree with what is said in JoulSauron's answer. The "beginner's" answer to the question is that it looks like a two-syllable word to us but it would be pronounced "bwo" without the accent as the "h" is silent. The basic rule is the stress is on the second last syllable unless you have a written accent to tell you otherwise. There are exceptions to this rule (for example words ending in certain letters) but it's a good place to start.