nachlassen
to lessen
To lose intensity, strength, quality, or performance; to become weaker or stop.
Gegen Abend ließ der starke Wind endlich nach.
Toward evening, the strong wind finally lessened.

to lessen / to reduce
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to lessen
To lose intensity, strength, quality, or performance; to become weaker or stop.
Gegen Abend ließ der starke Wind endlich nach.
Toward evening, the strong wind finally lessened.

'Nachlassen' (to lessen / to reduce) is a separable verb. The prefix 'nach-' comes at the end in a main clause. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Der Sturm hat endlich nachgelassen.
The storm has finally let up.
The meaning depends strongly on the context. If it is about weather, feelings, pain, or performance, 'nachlassen' usually means 'to become weaker'. If it is about money or prices, it means 'to give a discount'.
Meine Kopfschmerzen lassen langsam nach.
My headache is slowly easing.
The meaning 'to become weaker' is often used for things that lose intensity by themselves. Typical subjects are: pain, rain, wind, heat, strength, or concentration.
Nach einer Stunde ließ seine Konzentration deutlich nach.
After an hour, his concentration lessened noticeably.
When talking about a price reduction, the phrasing 'im Preis nachlassen' or 'beim Preis nachlassen' is often used. You can also simply ask: 'Können Sie noch etwas nachlassen?' (Can you reduce it a little more?)
Vielleicht lässt der Verkäufer noch etwas nach, wenn Sie bar bezahlen.
Maybe the seller will reduce the price a little more if you pay in cash.
to give
'sich geben' and 'nachlassen' can both mean that something becomes weaker or stops. 'sich geben' is often used for a problem, a strong feeling, or a natural phenomenon: excitement, pain, or a storm subsides. 'nachlassen' is broader and also fits performance, quality, pressure, or rain. 'sich geben' sounds like something calms down by itself. 'nachlassen' describes more generally that the intensity becomes less.

Am Abend lässt der Regen endlich nach.
In the evening, the rain finally lets up.
Keine Sorge, die Aufregung gibt sich nach ein paar Minuten.
Don't worry, the excitement will subside after a few minutes.