One person; a single person (used as a count of people).
このテーブルは一人用です。
This table is for one person.
会場にはゲストが一人増えて、合計で五人になった。
One more guest arrived at the venue, making five people in total.
1人（いちにん）ずつ名前を呼んでください。
Please call the names one person at a time.
Being alone; being by oneself (the state of having no one else present).
週末は一人で家でゆっくり過ごした。
I spent the weekend relaxing at home by myself.
子どもが一人で遊んでいるのを見守った。
I watched over the child who was playing alone.
一人でいるときの気楽さも好きだ。
I also like the freedom of being alone.
Being single; unmarried (often written as 独り).
彼はまだ独りだが、仕事に満足している。
He's still single, but he's satisfied with his job.
独り身を楽しむ人も多い。
There are many people who enjoy being single.
親の世話をしながら独りで暮らすのは大変だ。
Living alone while taking care of parents is tough.
As an adverb: by oneself; alone (doing something without others' help).
重要な決断は一人で下すべきではない。
You shouldn't make important decisions by yourself.
彼は一人で全部の料理を作った。
He cooked all the food by himself.
一人で出張に行くのは初めてだ。
It's my first time going on a business trip alone.
Used in negative sentences (e.g. '一人も〜ない') to mean 'not a single person' / 'not at all'.
昨日の集まりには一人も来なかった。
Not a single person came to yesterday's gathering.
彼のことを知っている人は一人もいない。
There is not a single person who knows him.
説明しても一人も理解してくれなかった。
Even after explaining, not a single person understood.