На ковре появилось пятно, поэтому я тёр его губкой.

A stain appeared on the carpet, so I rubbed it with a sponge.

Breakdown of На ковре появилось пятно, поэтому я тёр его губкой.

• я: I
• на: on
• ковёр: the carpet
• появиться: to appear
• его: it
• поэтому: so/therefore
• губка: the sponge
• пятно: stain
• тереть: to rub

Questions & Answers about На ковре появилось пятно, поэтому я тёр его губкой.

Why is it На ковре появилось пятно and not Пятно появилось на ковре?

Both are correct. На ковре появилось пятно is a very common “existential” pattern in Russian: you start with the location (on the carpet) and then introduce the new thing that appeared (a stain). It feels like “There appeared a stain on the carpet.”
Пятно появилось на ковре is more neutral when the stain is already the topic.

Why is появилось neuter singular?

Because the subject is пятно, which is neuter singular. In the past tense, Russian verbs agree in gender and number:

• пятно (neut. sg.) → появилось
• пятна (pl.) → появились

What case is на ковре, and why is it ковре?

На + “static location” uses the Prepositional case (often called “locative” in this context).
ковёр (dictionary form, nominative) changes to ковре in the prepositional:

• на ковре = “on the carpet” (location)
  If it were movement onto the carpet, you’d use на ковёр (accusative): положил на ковёр = “put onto the carpet.”

Why does ковёр become ковре (what’s happening to the spelling/stress)?

This is a regular declension change plus a stress shift. The noun is ковёр (stress on -ёр), but in ковре the stress moves: на коврЕ. The spelling ё is often written as е in ordinary text, but here it’s shown as ё to make pronunciation clear: ковёр.

What does поэтому do here, and why is there a comma before it?

поэтому means therefore/so, linking cause → result. Russian typically uses a comma before поэтому when it connects two clauses:
На ковре появилось пятно, поэтому я…
It’s like: “A stain appeared…, so I…”

Why is я тёр (imperfective) used instead of something like потёр / вытер / оттёр?

тёр is past tense of тереть (imperfective), which focuses on the process: “I was rubbing / I rubbed (for a while).” It doesn’t promise success.
If you want to focus on a completed result, Russian often uses a perfective verb:

• оттёр пятно = “rubbed the stain off (successfully)”
• вытер = “wiped (it) off / wiped (the surface) clean”
• потёр = “rubbed (a bit)” (often just the attempt/short action)

What exactly does тёр mean, and what’s the difference from чистил or мыл?

тереть / тёр = “to rub” (often with pressure and repeated motion).

• чистить = “to clean” (general cleaning, not necessarily rubbing)
• мыть = “to wash” (typically with water/soap)
  Using тёр suggests you were scrubbing/rubbing at the stain.

Why is it губкой and not губка?

Because губкой is the Instrumental case, used for the tool you do something with:

• тереть (чем?) губкой = “to rub with a sponge”
  Instrumental often answers “with what?” (чем?).

What does его refer to—the carpet or the stain?

Grammatically, его can refer to either ковёр (masculine) or пятно (neuter), because его is used for both masculine and neuter in the accusative/genitive forms. So the sentence is potentially ambiguous.
In real usage, context decides:

• If you mean the stain, you can make it clearer by saying я тёр пятно губкой.
• If you mean the carpet, you can say я тёр ковёр губкой or я тёр это место губкой (“this spot”).

Why isn’t пятно in the accusative after появилось?

Because появилось is intransitive here: a stain appeared. The stain is the subject (nominative), not a direct object. Russian doesn’t use an object case after появиться in this meaning.

How is the past tense formed in появилось and тёр?

Russian past tense is generally: verb stem + -л (plus gender/number endings), but there are irregularities.

• появиться → появи-л-ся → появилось (neuter singular; -сь becomes -лось after -л)
• тереть → тёр is an irregular past masculine form (no -л here)

Why is тёр written with ё?

тёр is pronounced with a stressed yo sound: [t’or]. In many texts, ё is often printed as е, but when it’s shown as ё, it helps you pronounce it correctly and distinguishes it from other forms.