
schnüren
to lace
To tighten and tie something with a shoelace, cord, or ribbon, especially shoes or boots.
Vergiss nicht, deine Wanderschuhe fest zu schnüren.
Don't forget to lace your hiking boots tightly.
to lace / tie
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to lace
To tighten and tie something with a shoelace, cord, or ribbon, especially shoes or boots.
Vergiss nicht, deine Wanderschuhe fest zu schnüren.
Don't forget to lace your hiking boots tightly.

to tie up
To wrap a package, bag, or bundle with a string and tie it tightly.
Sie schnürte ein Päckchen für ihre Freundin.
She tied up a small package for her friend.

to tighten someone's throat
To cause a feeling of fear, anxiety, or grief that physically feels like a tightening of the throat.
Die Angst vor der Prüfung schien ihm die Kehle zuzuschnüren.
The fear of the exam seemed to tighten his throat.
The verb 'schnüren' (to lace/tie) comes directly from the noun 'die Schnur' (string/cord). It describes the action of fastening something with a string or a cord-like band.
Kannst du mir helfen, das Paket mit einer Schnur zu schnüren?
Can you help me tie up the package with a string?
In this meaning, 'schnüren' (to lace) is almost always used in relation to shoes, boots, or clothing. Typical objects are 'die Schuhe' (the shoes), 'die Stiefel' (the boots), or 'das Mieder' (the corset/bodice).
Er setzte sich auf die Bank, um seine Laufschuhe zu schnüren.
He sat down on the bench to lace his running shoes.
When it comes to packaging, 'schnüren' (to tie up) is often combined with objects such as 'ein Paket' (a package), 'ein Päckchen' (a small package), or 'ein Bündel' (a bundle).
Früher hat man Pakete oft mit Paketschnur geschnürt.
In the past, people often tied up packages with parcel string.
In the idiom 'jemandem die Kehle zuschnüren' (to tighten someone's throat), the person who has the feeling is in the dative. The thing that triggers the feeling (e.g., fear) is the subject of the sentence. The separable verb 'zuschnüren' is often used here.
Die Traurigkeit schnürte ihr die Kehle zu.
The sadness tightened her throat.
to tie / bind
When talking about shoes, both binden and schnüren can be appropriate. binden particularly emphasizes tying the shoelaces into a knot or bow. schnüren more strongly includes tightening and tying the shoe with its laces.

Sie schnürt ihre Wanderschuhe vor dem langen Weg fest.
She laces her hiking boots tightly before the long walk.
Sie bindet ihre Schnürsenkel zu einer festen Schleife.
She ties her shoelaces into a firm bow.