“Amo” in praesenti est, “amabam” autem in imperfecto.

You can tell from their endings and tense markers:

• amo = am- + -o
  This is the 1st person singular present active indicative: I love / I am loving.

• amabam = ama- + -ba- + -m
  The marker -ba- is the usual sign of the imperfect in the 1st and 2nd conjugations. So amabam means I was loving or I used to love.

So the sentence is pointing out the difference between the simple present form amo and the imperfect form amabam.

Both are first person singular.

That means the subject is I in both cases:

• amo = I love
• amabam = I was loving / I used to love

Latin usually does not need a separate word for I, because the verb ending already tells you the person and number.

Because Latin verb endings usually already include the subject.

For example:

• amo already means I love
• amabam already means I was loving

If Latin wants to add ego (I), that is usually for emphasis or contrast, not because it is grammatically necessary.

Est is the verb is. It links each verb form with the tense being named.

So:

• amo in praesenti est = amo is in the present
• and the second half means amabam is in the imperfect

This is a normal use of sum, esse as a linking verb.

Because Latin often leaves out a word when it is easy to understand from the previous clause. This is called ellipsis.

So the full idea is:

• amo in praesenti est
• amabam autem in imperfecto est

But Latin does not need to repeat est, because the reader can easily supply it.

English does this too sometimes, as in Tom is tall, and Mary short.

Autem usually means however, but, on the other hand, or meanwhile, depending on context.

Here it marks a contrast:

• amo is in one tense,
• amabam, however / but, is in another.

So it helps set up the comparison between the two forms.

Because autem is normally postpositive in Latin. That means it usually comes after the first word or phrase of its clause, not before it.

So Latin prefers:

• amabam autem

rather than:

• autem amabam

This word order is very common with autem, enim, and some other particles.

They are in the ablative singular.

That is because they follow the preposition in, and here in means in in a static sense, so it takes the ablative.

So:

• in praesenti
• in imperfecto

both use the ablative.

Latin often uses in to place something within a category or state. Here the idea is that a verb form is in a certain tense.

So:

• in praesenti = in the present tense
• in imperfecto = in the imperfect tense

It is a standard grammatical way of speaking in Latin.

Originally, they are adjectives:

• praesens = present
• imperfectus = imperfect

But in grammatical language they can be used almost like nouns, meaning:

• the present tense
• the imperfect tense

You can also think of an understood noun such as tempore or tempore/temporo? Actually the usual idea is tempus (tense/time), with something like in [tempore] praesenti and in [tempore] imperfecto understood. In practice, learners usually just treat in praesenti and in imperfecto as standard grammar expressions.

Because Classical Latin has no articles equivalent to the, a, or an.

So Latin can simply say:

• in praesenti
• in imperfecto

and the context tells you that English should say:

• in the present tense
• in the imperfect tense

This is one of the basic differences between Latin and English.

Not in an ordinary descriptive sense. Here imperfecto is a grammatical term: it names the imperfect tense.

The word imperfectus literally does have the idea of unfinished or not completed, and that fits the traditional description of the imperfect as an ongoing, repeated, or incomplete past action. But in this sentence it is simply being used as the tense label.

There is nothing special about the third person here; the sentence just happens to use the first person singular forms.

Latin grammars often use amo because it is the basic, familiar form of the verb amo, amare. Once you know the pattern, the same contrast works for other persons too:

• amat = present
• amabat = imperfect

So the sentence is not saying that only amo can be present and only amabam can be imperfect. It is just using one pair of forms as examples.