المطر كثير في هذا الموسم.

In Arabic, the verb to be is usually not written or spoken in the present tense.

So:

• المطر كثير literally looks like the rain abundant/much
• but it means The rain is abundant or There is a lot of rain

This is very normal in Arabic nominal sentences.
If you wanted the past, you would use a verb, for example:

• كان المطر كثيرًا = The rain was abundant

Word by word:

• المطر = the rain
• كثير = much / abundant / plentiful
• في = in
• هذا = this
• الموسم = season

So the full sentence means something like:

• The rain is abundant in this season
• more naturally in English: There is a lot of rain this season

المطر has الـ because it refers to rain as a general known thing, not just some rain.

In Arabic, mass nouns and general concepts are often made definite when talking about them in a broad sense. So:

• المطر = the rain / rain in a general sense

English often says just rain, but Arabic commonly uses المطر here.

Because it agrees with المطر, and المطر is treated as a masculine singular noun.

So:

• المطر = masculine singular
• therefore كثير = masculine singular

If the noun were feminine, you would often expect a feminine form such as كثيرة.

It functions like a predicate adjective here.

So المطر كثير literally means:

• The rain is abundant
• The rain is plentiful

In natural English, we often translate that more idiomatically as:

• There is a lot of rain

So although كثير is an adjective, the whole sentence can sound like an English there is/there are expression.

In full vowelled formal Arabic, it actually can be written as:

• المطرُ كثيرٌ في هذا الموسمِ

Here كثيرٌ has ḍamma tanwīn because it is the predicate of a nominal sentence.

However, in normal unvowelled writing, those short endings are usually not shown, so you simply see:

• المطر كثير في هذا الموسم

Also, in pause or everyday pronunciation, many speakers do not clearly pronounce the final case endings.

في means in, so في هذا الموسم literally means in this season.

Arabic often uses في to express time periods, especially in formal language:

• في هذا الموسم = in this season
• natural English: this season

In some contexts, Arabic may omit في, but with this sentence, في هذا الموسم is clear and very standard.

This is a demonstrative phrase:

• هذا = this
• الموسم = the season

In Arabic, demonstratives like هذا often come before the noun:

• هذا الموسم = this season

Notice that the noun usually remains definite:

• هذا الموسم not
• هذا موسم

So literally it is this the-season, but in proper English we say this season.

Because in Arabic, when you use a demonstrative like هذا, the noun that follows is normally also definite.

So Arabic says:

• هذا الموسم = literally this the-season

That is the normal pattern. English does not do this, but Arabic does.

Other examples:

• هذا الكتاب = this book
• هذه المدينة = this city

Yes, you could, but it is slightly different in style.

• المطر كثير = Rain is abundant / There is a lot of rain
• الأمطار كثيرة = The rains are many / There are many rains, which sounds less natural in English but can work in Arabic depending on context

Arabic often uses المطر as a mass noun, which is very natural here. That is why المطر كثير is a very good sentence.

Yes, Arabic word order is somewhat flexible.

The basic sentence is:

• المطر كثير في هذا الموسم

You might also encounter:

• في هذا الموسم المطر كثير

This puts more emphasis on in this season.

Both are understandable, but the original order is straightforward and neutral.

It is a nominal sentence.

It starts with a noun:

• المطر

Then comes the predicate:

• كثير

Then an additional prepositional phrase:

• في هذا الموسم

So the structure is:

• subject/topic: المطر
• predicate/comment: كثير
• adverbial/prepositional phrase: في هذا الموسم

A careful pronunciation is roughly:

• al-maṭaru kathīrun fī hādhā al-mawsimi

In normal pause, many final case endings are dropped, so you may hear something closer to:

• al-maṭar kathīr fī hādhā al-mawsim

A rough English-style guide:

• al-MA-tar ka-THEER fee HAA-thaa al-MAW-sim

Notes:

• ṭ in مطر is an emphatic t
• dh in هذا sounds like the th in this
• th in كثير is like the th in think

The most natural translations are:

• There is a lot of rain this season.
• Rain is abundant this season.
• This season is very rainy. — this is a looser translation, not word-for-word

The closest literal translation is:

• The rain is abundant in this season.

But in natural English, There is a lot of rain this season sounds best.