La batería recargable dura todo el día.

Because batería is a feminine noun in Spanish, so it takes the feminine article la.

• la batería = the battery
• una batería = a battery

The ending -a often signals a feminine noun, and in this case that pattern fits.

Recargable means rechargeable.

In Spanish, many adjectives commonly come after the noun, unlike in English:

• la batería recargable = the rechargeable battery

That word order is very normal in Spanish. English usually says rechargeable battery, but Spanish often prefers battery rechargeable in that literal order.

Recargable is an adjective ending in -e, so its masculine and feminine singular forms are the same.

• el cargador recargable
• la batería recargable

If it were plural, it would change to recargables:

• las baterías recargables

So it does agree with the noun, just not by changing for gender in the singular.

Here, dura comes from the verb durar, which means to last.

So:

• dura todo el día = lasts all day

Be careful: dura can also be an adjective meaning hard or tough in other contexts, but here it is clearly the verb.

Because dura is the third-person singular present tense form of durar.

The subject is la batería recargable, which is singular, so the verb must match it:

• La batería recargable dura... = The rechargeable battery lasts...

Compare:

• yo duro
• tú duras
• él/ella/usted dura

So dura means it lasts in this sentence.

Because día is singular, so todo also stays singular:

• todo el día = all day / the whole day

If the noun were plural, then you would use todos:

• todos los días = every day / all the days

So:

• todo el día = one whole day
• todos los días = every day, repeatedly

In Spanish, expressions like todo el día, toda la noche, todo el tiempo usually include the definite article.

So the natural phrase is:

• todo el día = all day

Without the article, todo día would sound unnatural in standard Spanish.

It can mean either all day or the whole day, depending on the context. In English those are very close, and Spanish uses todo el día for both ideas.

Examples:

• La batería dura todo el día. = The battery lasts all day.
• Estuve ocupado todo el día. = I was busy the whole day / all day.

Spanish often leaves subject pronouns out when they are not needed, because the verb form already gives enough information.

So instead of saying:

• La batería recargable ella dura todo el día

Spanish simply says:

• La batería recargable dura todo el día

Adding ella here would sound unnecessary and unnatural.

Yes. That would simply mean:

• La batería dura todo el día. = The battery lasts all day.

Adding recargable just gives extra information about what kind of battery it is:

• la batería = the battery
• la batería recargable = the rechargeable battery

Both are grammatically correct.

It would become:

• Las baterías recargables duran todo el día.

Notice the changes:

• la → las
• batería → baterías
• recargable → recargables
• dura → duran

Everything agrees with the plural subject.

It can mean battery, but it also has other meanings depending on context. For example, batería can also mean a drum set.

So:

• La batería del teléfono = the phone battery
• Toca la batería = He/She plays the drums

In your sentence, because of recargable and dura todo el día, it clearly means battery.

The stress is on the -rí- syllable: ba-te-RÍ-a.

The written accent shows that the stress does not follow the most basic default pattern. It also helps show that í-a is pronounced in separate syllables.

So it sounds roughly like:

• bah-teh-REE-ah

That accent mark is important and should be written: batería, not bateria.