Learn Hardcore Russian: Широкая лестница кажется более безопасной, чем узкая. - A wide staircase seems safer than a narrow one.

In Russian, when you use verbs like казаться (to seem), быть (to be, in the past/future), становиться (to become), the “resulting state” or “quality” is often put in the instrumental case.

широкая лестница – nominative (subject)
кажется – verb казаться, 3rd person singular
более безопасной – instrumental (what it seems as)

Compare:

Лестница кажется безопасной. – The staircase seems safe.
Он кажется уставшим. – He seems tired.

So безопасной is feminine singular instrumental of безопасный, agreeing with лестница and used because of кажется.

Why is широкая лестница in the nominative, not instrumental?

Широкая лестница is the subject of the sentence, so it must be in the nominative case.

Russian basic pattern here is:

[Subject in nominative] + кажется + [description in instrumental]

So:

Широкая лестница (nominative) – the wide staircase (subject)
кажется более безопасной (instrumental) – seems safer

Only the predicative part (what it seems) goes into the instrumental; the subject always stays nominative.