An abide means to accept or put up with a situation, often for a long time. It's like living with something, rather than fighting it.
When people say they'll abide by the rules, they mean they agree to follow them and won't try to change them. If there's a law or a decision that you don't love, but you have to live with it, abiding means accepting it and moving on. Some people talk about abiding in their faith or religion – they stick to its teachings even if they're not easy to follow. It can also mean tolerating something difficult, like living near noise pollution, for example. You abide by the rules of a game or a social situation, which means you play along and do what's expected of you.
How common is "abide"?
Word abide is considered uncommon in modern English. It has a balanced usage among all categories: speech, fiction, newspapers and academic texts.
Definitions
verb
(transitive) To endure without yielding; to withstand.
Example: The old oak tree abides the wind endlessly.
(transitive) To bear patiently.
Example: "I never could abide shoemakers," said an old servant,—and it ended in her marrying one.
(transitive) To pay for; to stand the consequences of.
Used in a phrasal verb: abide by (“to accept and act in accordance with”).
Example: The new teacher was strict and the students did not want to abide by his rules.
(intransitive, obsolete) To wait in expectation.
(intransitive, obsolete) To pause; to delay.
(intransitive, archaic, Scotland) To stay; to continue in a place; to remain stable or fixed in some state or condition; to be left.
(intransitive, archaic) To have one's abode.
(intransitive, archaic) To endure; to remain; to last.
(transitive, archaic) To stand ready for; to await for someone; watch for.
(transitive, obsolete) To endure or undergo a hard trial or a task; to stand up under.
(transitive, archaic) To await submissively; accept without question; submit to.