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.

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
'binden' and 'schnüren' are close in meaning when it comes to shoelaces, cords, or ribbons. 'binden' is more general and means that you fasten something with a ribbon or string, often with a bow or knot. 'schnüren' puts more emphasis on tightening a cord and thereby closing something or pressing it together, especially shoes, boots, or a package. So you can 'Schuhe binden' or 'Schuhe schnüren' (tie/lace shoes). 'schnüren' sounds more precise when tightening the cord is important.

Vor der Wanderung schnürt Max seine Stiefel besonders fest.
Before the hike, Max laces his boots especially tightly.
Das Kind kann seine Schuhe schon allein binden.
The child can already tie his shoes by himself.