Høsten bliver bedre, jo mere sol haven får i juli og august.

Here jo mere is part of the Danish pattern for the more ..., the ....

So:

• jo mere sol ... = the more sun ...
• combined with bedre = the better

Also, this jo is not the everyday jo meaning something like yes or indeed. In this sentence it is a grammatical marker used in comparisons.

Both versions are possible.

The sentence you have starts with the main idea:

• Høsten bliver bedre, jo mere sol haven får i juli og august.

A very common alternative is the more balanced comparative structure:

• Jo mere sol haven får i juli og august, jo bedre bliver høsten.

In English, that is like the difference between:

• The harvest gets better, the more sun the garden gets and
• The more sun the garden gets, the better the harvest gets

The comma separates the two linked clauses.

Because mere sol is the thing being compared, so it comes right after jo.

The basic clause is:

• Haven får mere sol i juli og august. = The garden gets more sun in July and August.

In the comparative structure, Danish moves the compared element forward:

• jo mere sol haven får ...

So:

• sol is the object
• haven is the subject
• får is the verb

That is why it is sol haven får, not the more neutral haven får mere sol.

Bliver means becomes / gets, so it shows change or improvement.

• Høsten bliver bedre = The harvest becomes better / gets better
• Høsten er bedre = The harvest is better

In this sentence, the idea is that more sun leads to a better result, so bliver fits naturally.

They are the Danish definite ending, equivalent to English the.

• høst = harvest

• høsten = the harvest

• have = garden
• haven = the garden

Danish often puts definiteness at the end of the noun instead of using a separate word like the.

Får is from at få, which usually means to get or to receive.

So:

• haven får sol = the garden gets sun

This is a very natural way to talk about weather, light, water, and growing conditions in Danish.

Because sol here means sun / sunlight as a mass noun.

Danish often uses no article with mass nouns in this kind of sentence:

• mere sol = more sun
• mere vand = more water
• mere regn = more rain

So mere sol works like English more sun, not more a sun.

Because Danish normally uses i with months when meaning in a certain month.

• i juli = in July
• i august = in August

So i juli og august simply means in July and August.

In this sentence, it means harvest.

In modern Danish, efterår is the usual word for autumn. The word høst can sometimes be connected with the season historically or poetically, but here the natural meaning is clearly the harvest.