This is the adjective "wearing", and it does not mean "putting clothes on" — that is the -ing form of the verb, a different thing wearing the same coat. As an adjective, "wearing" means it slowly uses you up. Something wearing makes you tired, or tired and a bit annoyed, not in one big shock but little by little, over hours or weeks.

The picture behind it is real wearing: a stone step that thousands of feet have worn down, a shoe sole rubbed thin. The thing is not smashed — it is just quietly reduced by contact happening again and again. That is exactly the feeling. A wearing job is not one terrible day; it is the same small demands, every day, until there is less of you left.

So you use it for things that repeat and drain: a long illness in the family, a noisy flat, constant travelling, a person who complains all the time. "He is very kind, but he can be quite wearing." Said about a person, it is a gentle way of saying "being with them costs me energy" — polite, mild, and quite British-sounding. English people love it for this reason: it complains without insulting anyone.

It is a bit formal and more common in writing and in older or careful speech. Younger speakers more often say "draining", "exhausting", or "tiring". Compare the neighbours: "tiring" is plain and physical (a tiring walk); "exhausting" is strong and total; "wearing" is medium, slow, and carries that hint of irritation. You will also meet "wearing thin" — "my patience is wearing thin" — the same picture, the same idea.