Questo coccio viene da una brocca.

Because coccio is a masculine singular noun, so the demonstrative must match it:

• questo coccio = this shard
• questa brocca = this jug

In Italian, words like this change form depending on the gender and number of the noun.

Here coccio means a piece of broken pottery, potsherd, or ceramic shard.

It is more specific than a general word like pezzo (piece).
So coccio suggests that the object is a fragment from something ceramic that broke.

Viene da literally means comes from.
Here it expresses origin: the shard originated from a jug.

• viene = comes
• da = from

So Questo coccio viene da una brocca means that this fragment comes from, or belonged to, a jug.

A close synonym is proviene da, which is a bit more formal:

• Questo coccio proviene da una brocca.

Viene is the 3rd person singular present indicative of venire (to come).

Conjugation:

• io vengo
• tu vieni
• lui/lei viene
• noi veniamo
• voi venite
• loro vengono

It is singular because the subject is questo coccio, which is singular.

Because brocca is a feminine singular noun, so the indefinite article is una.

Compare:

• un coccio = a shard
• una brocca = a jug

Italian articles must agree with the noun in gender and number.

Yes, brocca usually means jug, pitcher, or sometimes a handled container used for liquids.

The exact English choice depends on context, but jug is a very natural translation here.

Normally, no. È da una brocca does not sound natural for expressing origin in this context.

To say that a fragment comes from something, Italian usually uses:

• viene da
• proviene da

So the natural sentence is:

• Questo coccio viene da una brocca.

Yes, but the meaning changes slightly.

• Questo coccio viene da una brocca. = This shard comes from a jug.
• Il coccio viene da una brocca. = The shard comes from a jug.
• Un coccio viene da una brocca. = A shard comes from a jug.

Questo points to a specific shard near the speaker or already identified.

The given order is the most neutral and natural:

• Questo coccio viene da una brocca.

Italian word order is somewhat flexible, but changing it usually adds emphasis or sounds more literary/marked. For example:

• Da una brocca viene questo coccio.

This is possible, but much less neutral. For a learner, the original order is the best one to use.

Coccio is pronounced roughly KOT-cho.

A few useful points:

• cc before i gives a ch sound, like in church
• so coccio sounds like KOT-cho
• brocca has a hard k sound: BROK-ka

So roughly:

• questo coccio → KWE-sto KOT-cho
• brocca → BROK-ka

Pezzo is a very general word meaning piece.
Coccio is more specific: a broken pottery fragment.

So:

• pezzo = piece, part, chunk, fragment in general
• coccio = shard of pottery/ceramic

In this sentence, coccio is the better word because it tells you the material and the fact that it is broken.

No. Although venire literally means to come, venire da is also often used for origin or source, not just movement.

In this sentence, the shard is not literally walking over from the jug. The phrase means that the shard originates from the jug.

So Italian often uses a movement verb in places where English may prefer is from or comes from.