das Bedürfnis
need
The wish or desire for something that you need or consider important.
Nach der langen Wanderung hatte ich das dringende Bedürfnis nach einer Dusche.
After the long hike, I had an urgent need for a shower.

need
Loading your saved state.
need
The wish or desire for something that you need or consider important.
Nach der langen Wanderung hatte ich das dringende Bedürfnis nach einer Dusche.
After the long hike, I had an urgent need for a shower.

'Das Bedürfnis' (need) is a noun derived from the increasingly old-fashioned verb 'bedürfen' (to need something). The ending '-nis' often forms nouns from verbs or adjectives that describe a state or a result.
Jeder Mensch hat Grundbedürfnisse wie Essen und Schlafen.
Every person has basic needs such as eating and sleeping.
The wish or desire is usually expressed with the preposition 'nach' and the dative. The typical construction is: 'das Bedürfnis nach etwas haben' (to have a need for something).
Nach dem langen Flug hatte sie ein starkes Bedürfnis nach Schlaf.
After the long flight, she had a strong need for sleep.
Common verbs used with 'Bedürfnis' (need) are 'ein Bedürfnis haben' (to have a need), 'ein Bedürfnis verspüren' (to feel a need), or 'ein Bedürfnis befriedigen' (to satisfy a need).
Er verspürte das Bedürfnis, mit jemandem zu reden.
He felt the need to talk to someone.
The phrase 'sein Bedürfnis verrichten' (to relieve oneself) is a euphemism, meaning a polite and indirect way of saying 'auf die Toilette gehen' (to go to the toilet). It is often used in more formal contexts or when talking about animals and small children.
Gibt es hier in der Nähe eine Möglichkeit, sein Bedürfnis zu verrichten?
Is there somewhere nearby where one can relieve oneself?
desire / pleasure
'die Lust' and 'das Bedürfnis' both express that you want something. 'Lust' is usually more spontaneous and often pleasant: you may have Lust auf Eis, Musik oder einen Film (feel like ice cream, music, or a movie). 'Bedürfnis' sounds more serious and stronger because it is about something you need or consider important, such as rest, safety, or sleep. Learners may confuse the words because both describe a desire. If it is only about a spontaneous wish, 'Lust' fits better. If something is important for well-being, 'Bedürfnis' fits better.

Nach dem Unterricht hat Ali ein starkes Bedürfnis nach Ruhe.
After class, Ali has a strong need for quiet.
Am Montag hatte sie Lust auf etwas Süßes.
On Monday, she felt like having something sweet.