Some languages use changes to the ending of a noun to mark the role of nouns in the sentence - for example whether they are the one doing the verb or whether they are the one the verb acts upon. It's a bit like how verbs change their ending to show whether they are in the present or past tense.
So, it's vala when the man is the one doing the verb. vala urnes = the man sees
And it's vale when the man is the one who the verb acts upon. Here what I see is the man, so it has to change its ending, so we get vale to show it is the one being seen.
vala urnes = the man sees
vale urnes = he/she/it sees the man
A few grammar terms
The roles the nouns can play are called cases. When the noun is doing the verb, it is said to be in the nominative case; vala is an example. When it is directly being acted upon by the verb (similar to English's direct object) it is said to be in the accusative case; vale is an example.
The way a noun changes follows a pattern, and all the patterns get called declensions. In High Valyrian, the pattern they follow will depend upon what the word ending is in the nominative singular, and whether they are lunar, solar, terrestrial, or aquatic. There are a few declension classes in High Valyrian, but they seem fairly regular (to me anyway) so they are not so difficult as the first glance at the tables may make them appear: https://wiki.dothraki.org/High_Valyrian_Noun_Declensions#Lunar-type:_vala
There are eight cases in High Valyrian, but the ones which appear most frequently are the nominative and accusative cases (in the singular and plural). So these are the ones to get to know well. :)