ככל שאני מתרגלת יותר, כך טווח התנועה שלי משתפר.

It means the more ... the more ... or the more ... the better ..., depending on context.

So:

• ככל שאני מתרגלת יותר = the more I practice
• כך טווח התנועה שלי משתפר = the more my range of motion improves / my range of motion improves accordingly

This is a very common Hebrew pattern for showing a correlation between two things.

מתרגלת is the feminine singular present-tense form.

So the sentence is being said by a female speaker:

• אני מתרגלת = I practice (female speaker)
• אני מתרגל = I practice (male speaker)

If a man were saying the same sentence, it would be:

ככל שאני מתרגל יותר, כך טווח התנועה שלי משתפר.

שאני is a combination of:

• ש־ = that / as / when (depending on context)
• אני = I

So שאני literally looks like that I, but in this structure it is just part of the natural phrasing after ככל.

In other words:

• ככל שאני מתרגלת יותר = literally something like to the extent that I practice more
• natural English: the more I practice

You do not need to translate ש separately every time; just learn ככל ש... כך... as a set pattern.

Because יותר means more, and in Hebrew it often comes after the word it modifies.

Here:

• מתרגלת יותר = practice more

This is very natural Hebrew word order.

Compare:

• אני לומדת יותר = I study more
• אני הולכת יותר = I walk more

So in this sentence, יותר modifies the action of practicing.

Literally, it is:

• טווח = range
• התנועה = the movement

Together, טווח התנועה means range of motion.

This is a construct phrase in Hebrew, where two nouns are linked:

• טווח התנועה = the range of motion
• not טווח של התנועה in this case

This structure is very common in Hebrew.

Because Hebrew uses a special noun-linking structure called סמיכות (the construct state).

In טווח התנועה:

• the first noun (טווח) stays without ה־
• the second noun (התנועה) carries the definiteness

So:

• טווח תנועה = a range of motion
• טווח התנועה = the range of motion
• טווח התנועה שלי = my range of motion

Adding שלי after the whole phrase is the normal way to say my here.

משתפר means improves or gets better.

It comes from the verb להשתפר = to improve / to get better.

So:

• טווח התנועה שלי משתפר = my range of motion is improving / improves / gets better

Notice that this is an intransitive idea: the range of motion itself is getting better.

That is why Hebrew uses להשתפר rather than לשפר here.

This is an important distinction:

• משתפר = improves / gets better
• משפר = improves something

Examples:

• המצב משתפר = the situation is improving
• אני משפרת את המצב = I am improving the situation

In your sentence, טווח התנועה is the thing that is getting better by itself, so משתפר is the correct form.

Because משתפר agrees with טווח, not with אני.

• אני is the speaker, and that affects מתרגלת
• טווח התנועה שלי is the subject of the second clause, and טווח is a masculine singular noun

So:

• אני מתרגלת → feminine speaker
• טווח התנועה שלי משתפר → masculine noun טווח

If the subject in the second clause were a feminine noun, the verb would change accordingly.

Yes. Both verbs are in the present tense:

• מתרגלת = practicing / practice
• משתפר = improving / improves

In Hebrew, the present tense is often used for:

• general truths
• habits
• ongoing situations

So this sentence can mean something like:

• The more I practice, the more my range of motion improves
• As I practice more, my range of motion gets better

Sometimes in casual Hebrew, speakers may omit כך, especially if the meaning is clear. But with this pattern, ככל ... כך ... is the full and neat form.

So:

• ככל שאני מתרגלת יותר, כך טווח התנועה שלי משתפר. = full, standard, clear

Leaving out כך might still be understood, but the sentence is more complete and polished with it.

Yes: the main idiomatic part is the structure ככל ש... כך....

A learner should probably remember the sentence as built from three chunks:

• ככל ש... = the more...
• יותר = more
• כך... = so / accordingly / the more...

This makes it easier to build similar sentences, for example:

• ככל שאני לומדת יותר, כך אני מבינה יותר.
  The more I study, the more I understand.

• ככל שמתאמנים יותר, כך משתפרים.
  The more one trains, the more one improves.