What does "+1 sword" or "-3 ring" mean?

What do these numbers next to the type of item (specific example: a cursed -3 ring of protection) mean in Crawl? I've tried all sorts of Google queries and I've checked the in-game manual, but I can't find anything. I think I've seen some with two numbers ("a +2/+1 sword"), what does that mean?

In regards to weapons, the first number is accuracy and the second number is damage (up through 0.14.2; in 0.15, weapons have just a single number for both accuracy and damage), as you and Han already pointed out.

The -3 ring of protection means that 3 is subtracted from your Armor. Rings and Amulets of protection always have a number, and it always affects Armor. Rings of slaying always have a number, and it always affects accuracy and damage. I am not aware of other numeric modifiers on jewelry. Armor items can also have numbers like this, which intuitively also affects armor.

Well, these bonuses probably started because of the system introduced in the D&D and AD&D table-top role-playing games.

Usually, a +2/+1 sword would mean a bonus of +2 to hit your target, and a bonus damage of +1 when you do hit your target.

Hence, cursed weapons usually come with negative bonuses because they cause you to miss more often or hit with less damage.

What I've just written above are the "norm" concerning magical items/ weapons/ armor etc. when it comes to role-playing games. It should be the same in Crawl's case.

Try checking the wiki for Crawl... I took a quick glance. Seems to have what you are asking for.