Some very common homophones that can confuse English language learners are buy/by, your/you're, there/their/they're and to/too/two. Homophones are very common in English and can cause confusion, especially to those new to the language.
Homophones are words that sound similar but are spelled differently and have different meanings. For example, there/their/they're. "There" is used primarily as a means of direction. For example: "The car is parked over there." "Their" is used to show ownership of another party. For example: "John went over to their house for dinner." "They're" is a contraction combining "they" and "are" to show an action of another party. For example: "They're running away from the zombies."
Homophones can also have the same spelling, but different meanings. A very common example is the word rose, which could mean the flower or to rise in the past tense. These are also referred to as homographs, due to their similar spelling, but this is a technical term mostly used by scholars.
Some homophones arise from regional pronunciation. For example, the words affect and effect. Affect is pronounced with a long "ah" sound, while effect is pronounced with the short "eh" sound. In many regions these two sounds can be blended together or used interchangeably, causing the two words to appear as homophones.