spannen
to stretch / tighten
To pull something tight or stretch it so that it is under tension.
Er spannte ein Seil zwischen den beiden Bäumen.
He stretched a rope between the two trees.

to stretch / tighten / peep
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to stretch / tighten
To pull something tight or stretch it so that it is under tension.
Er spannte ein Seil zwischen den beiden Bäumen.
He stretched a rope between the two trees.

The verb 'spannen' is the root of the noun 'die Spannung' (tension, suspense) and the adjective 'spannend' (exciting). All of these words have the basic idea of tension or tightness.
Die Spannung vor dem Finale war riesig.
The tension before the final was enormous.
The past participle 'gespannt' is very often used as an adjective and means 'curious' or 'eager with expectation'. The preposition used with it is 'auf' with the accusative.
Ich bin gespannt, wie die Geschichte ausgeht.
I'm curious to see how the story ends.
In the meaning 'straff ziehen' (to pull tight), 'spannen' is often combined with things that can be stretched. Typical examples are: 'ein Seil spannen' (to stretch a rope), 'ein Netz spannen' (to spin/stretch a net), 'eine Feder spannen' (to cock/tension a spring), or 'die Muskeln anspannen' (to tense the muscles).
Die Spinne hat ihr Netz zwischen den Ästen gespannt.
The spider stretched its web between the branches.
When clothing is too tight, the item of clothing is the subject of the sentence. Often 'an' or 'am' plus dative is used to indicate where it presses.
Das neue Hemd spannt an den Schultern.
The new shirt feels tight at the shoulders.
The idiom 'jemanden auf die Folter spannen' (to keep someone in suspense) is a fixed unit. The person being made curious is always in the accusative.
Nun sag schon, wer gewonnen hat! Spann mich nicht auf die Folter!
Come on, tell us who won! Don't keep me in suspense!
In the meaning 'heimlich beobachten' (to observe secretly), 'spannen' is a colloquial word with a strongly negative and derogatory meaning.
Es ist strafbar, Leute in ihren Wohnungen zu bespannen.
It is illegal to spy on people in their apartments.
to press / hug
'spannen' and 'drücken' can both have to do with an unpleasant feeling of pressure. 'spannen' is often used when something is too taut or too tight, for example clothing or a bandage. It describes more of a pulling or tension across a surface. 'drücken' means more of a pressure on a specific spot or a burden that weighs on someone physically or emotionally. A shoe, for example, can 'drücken' because it hurts in one spot. If something fits tightly and feels taut, 'spannen' is better; if something presses on a spot or weighs on someone, 'drücken' is better.

Nach dem Essen spannt die Hose ein bisschen.
After the meal, my pants feel a little tight.
Der neue Schuh drückt mich an der Ferse.
The new shoe is pressing on my heel.