や lists a few items out of more — 'things like A and B'. It is the open-ended counterpart to と.
Also known asya particleや particlelisting examplesya vs to
や lists a few nouns as examples — “A, B and so on”. と gives the complete list.
はこの なかに てがみや しゃしんが あります。
In the box there are letters, photos and so on.
つくえの うえに ほんや ノートなどが あります。
On the desk there are books, notebooks and the like.
や picks a few items and implies there is more. など at the end of the list makes that explicit. Compare と: 手紙と 写真 = letters and photos, nothing else.
In the textbooksMinna I, lesson 10
や lists nouns as examples — “A and B (among others)”, unlike と, which gives a complete list.
きょうとや ならへ いきました。
I went to Kyoto and Nara (among other places).
つくえの うえに ほんや ノートが あります。
On the desk there are books, notebooks and so on.
や joins nouns but implies the list is partial (“and so on”), much like 〜たり〜たり does for verbs. Use と for an exhaustive “A and B”.
It is often paired with …など (“…and the like”) at the end of the list.
In the textbooksGenki I, lesson 11