To stress a syllable in a word is to make its sound slightly more prominent, more emphasized, than the other syllables. Ossetian/Иронау has a rule, but unlike English, it adds another layer, one level higher in fact, at the phrase/clause level. It is important to understand this theory because in practice there is a difference between how the language sounds when spoken, versus how it looks when written.
The rule is actually the same at both levels, but at the phrase/syllable level it bears a bit more thought because it involves all the syllables in your sentence.
In Ossetian/Иронау, the rule of syllable stress is regulated by a distinction between two subsets of the vowel inventory, 'strong' and 'weak'. This system comes from the Old-Iranian Language, and was based on 'long' and 'short' vowels. These long and short vowels followed a broad, cross-linguistic trend (amongst languages that make such a distinction), where long vowels were held for twice the length of the short vowels. Other languages that make this distinction are, for example, Latvian and Finnish. These languages indicate this long/short difference in their writing in different ways, however. The Latvian language uses diacritic marks, such as in the word māja 'house', while Finnish uses vowel duplication, such as in the word kuusikymmentäviisi 'sixty-five'.
There are two weak vowels in Ossetian/Иронау, 'ӕ' and 'ы', the rest falling into the strong category. The rule is that if there is a strong vowel in the first syllable, then that syllable receives the stress; but if there is a weak vowel in the first syllable, then the second syllable receives the stress. Ossetian/Иронау has expanded on this by adding a secondary rule, where words with the stress on the second syllable can express definiteness by shifting the emphasis to the first syllable, the classic example is found in the word for axe, Фӕрӕт 'an axe', Фӕрӕт 'the axe'. Words that already have emphasis on the first syllable do not receive the same treatment in reverse.
Now that you understand the basic rule about syllable stress, you can take it and apply it to entire sentences; if there is a strong vowel in the first word, that word receives the stress, if not, then the second word receives it. This is where you need to understand the difference between what is written and spoken, because the writing does not typically demonstrate which words/syllables get the stress.
In his writing, Abaev gives an example:
You can see that in certain circumstances, phrase stress can be the exact same as syllable stress, depending on the nature of the two words being linked.
For my own personal studying, I really like to think about this subject when I'm listening to/reading stories on the app Ирон Чиныг. The written stories allow you to easily follow along and catch where the phrase stress is different from the writing.