Learn Swedish: Det är silket som hon är varsam med. - It is the silk that she is careful with.

Because varsam describes hon (she), it takes the base en-word form here. If it described a plural noun, it would become varsamma. Notice the double m in varsamma: Swedish doubles the consonant to keep the preceding a short when adding the plural -a ending! If it described an ett word, it would be varsamt.

Why is the preposition med placed at the very end of the sentence?

Just like in English, Swedish often leaves the preposition at the end of a relative clause. The word med belongs to the phrase vara varsam med (to be careful with). Because the object of the preposition (silket) was moved to the beginning of the sentence for emphasis, med gets left behind at the end.

Why does silket end in -t instead of the usual -et for definite ett words?

The noun ett silke (a silk) already ends in a vowel. For ett words that end in a vowel, you usually just add -t to make them definite, resulting in silket (the silk). Adding -et would create an awkward double vowel.

Could I just say Hon är varsam med silket? What does the Det är ... som structure add here?

Yes, you could! Using Det är silket som (It is the silk that) is a cleft sentence used to add emphasis. It highlights that she is careful with the silk specifically, perhaps in contrast to something else she might be handling roughly.