La table est couverte de miettes.

Because table is a feminine noun in French, so it takes the feminine singular article la.

• la table = the table
• une table = a table

This is something you simply have to learn with the noun: in French, every noun has grammatical gender.

Because couverte agrees with table, which is feminine singular.

The basic form is:

• masculine singular: couvert
• feminine singular: couverte
• masculine plural: couverts
• feminine plural: couvertes

So:

• Le sol est couvert de poussière.
• La table est couverte de miettes.

This agreement happens because couvert/couverte is functioning like an adjective here, even though it comes from the verb couvrir (to cover).

The finite verb is est, from être (to be).

The full expression est couverte means is covered.

So the sentence is built like this:

• La table = subject
• est = is
• couverte de miettes = covered in crumbs / covered with crumbs

It is best understood here as a past participle used adjectivally, or as part of a passive-style structure.

In practical terms, for a learner, it means:

• couvrir = to cover
• couvert/couverte = covered

So La table est couverte de miettes means The table is covered in crumbs.

You do not need to worry too much about the label at first. The important thing is that couvert(e) de is a very common pattern in French.

Because French normally uses couvert de to say what something is covered with.

So:

• couvert de neige = covered in snow
• couvert de poussière = covered in dust
• couverte de miettes = covered in crumbs

Using avec would sound unnatural here.
A native English speaker may expect with, but French prefers de after couvert in this meaning.

After couvert(e), French usually uses plain de, not de + article.

So the pattern is:

• couvert de sable
• couvert de feuilles
• couverte de miettes

Even though in English we might say covered with crumbs, French does not normally say couverte des miettes here.

Miettes means crumbs.

The singular is miette, meaning crumb, but French very often uses it in the plural because crumbs usually appear as many little pieces.

Examples:

• une miette = a crumb
• des miettes = crumbs

So de miettes here means in crumbs or with crumbs all over it.

Because the idea is that the table has many crumbs on it, not just one.

If there were only one crumb, you could say:

• La table est couverte d’une miette.

But that would sound odd, because covered in one crumb is not very logical. In real usage, miettes is much more natural.

Not exactly. They are close in meaning, but the focus is different.

• La table est couverte de miettes
  = The table is covered in crumbs.
  This emphasizes the amount or the messy condition.

• Il y a des miettes sur la table
  = There are crumbs on the table.
  This simply states that crumbs are present.

So the first sentence sounds stronger and more descriptive.

A natural pronunciation is approximately:

la tabl eh koo-VEHRT duh myett

A few notes:

• table sounds roughly like tabl
• est is usually pronounced eh
• couverte has the stressed feeling on vert: koo-VEHRT
• de often sounds like a light duh
• miettes sounds roughly like myett

Also, the final s in miettes is silent.

Yes, you can, but it is a bit different in tone.

• couverte de miettes = covered in crumbs
• recouverte de miettes = covered over with crumbs / completely covered in crumbs

Recouverte can sound slightly more emphatic or more complete.
In everyday French, couverte de miettes is already very natural.

Then couvert would also become plural to agree with it.

Examples:

• Les tables sont couvertes de miettes.
  = The tables are covered in crumbs.

Here:

• les tables = feminine plural
• sont = are
• couvertes = feminine plural form

This is a good example of adjective/past-participle agreement after être.