
senken
to lower
To actively move something downward or bring it into a lower position.
Er senkte seinen Blick, als er angesprochen wurde.
He lowered his gaze when he was spoken to.
to lower
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to lower
To actively move something downward or bring it into a lower position.
Er senkte seinen Blick, als er angesprochen wurde.
He lowered his gaze when he was spoken to.

to reduce
To reduce or decrease a level, value, price, or amount.
Die Zentralbank hat den Leitzins gesenkt, um die Wirtschaft anzukurbeln.
The central bank lowered the key interest rate to stimulate the economy.

to descend
To go downward, sink, or fall by itself.
Der Nebel senkte sich langsam über das Tal.
The fog slowly descended over the valley.
'Senken' (to lower) is a transitive verb. This means it always needs an accusative object—that is, someone or something that is actively being lowered.
Die Firma muss die Kosten senken, um wettbewerbsfähig zu bleiben.
The company has to reduce costs in order to remain competitive.
In the meaning 'nach unten bewegen' (to move downward), 'senken' (to lower) is often used with body parts or the voice. Typical phrases are 'den Kopf senken' (to lower one's head), 'den Blick senken' (to lower one's gaze), or 'die Stimme senken' (to lower one's voice).
Als sie die schlechte Nachricht hörte, senkte sie den Kopf.
When she heard the bad news, she lowered her head.
In the meaning 'reduzieren' (to reduce), 'senken' (to lower/reduce) is used very often in economic or scientific contexts. You can 'senken' prices, costs, taxes, interest rates, or even a fever.
Der Supermarkt hat die Preise für viele Produkte gesenkt.
The supermarket reduced the prices of many products.
When something goes downward by itself, the reflexive form 'sich senken' (to descend/sink) is used. This is often the case with natural phenomena, such as 'der Nebel' (the fog), 'die Nacht' (the night), or 'die Dunkelheit' (the darkness).
Die Nacht senkte sich über die Stadt.
Night descended over the city.
to press / hug
When talking about prices and costs, drücken and senken both mean that the value becomes smaller. Senken describes the reduction neutrally and directly. Drücken presents it more as the result of pressure or deliberate bargaining.

Wegen der geringeren Kosten senkt der Händler den Preis auf 800 Euro.
Because of the lower costs, the dealer lowers the price to 800 euros.
Mit harten Verhandlungen drückt der Händler den Preis auf 800 Euro.
Through tough negotiations, the dealer pushes the price down to 800 euros.