
leisten
to perform
To accomplish, achieve, or provide something that often requires effort or ability.
Die Mitarbeiter haben im letzten Quartal hervorragende Arbeit geleistet.
The employees performed excellent work in the last quarter.
to perform / afford
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to perform
To accomplish, achieve, or provide something that often requires effort or ability.
Die Mitarbeiter haben im letzten Quartal hervorragende Arbeit geleistet.
The employees performed excellent work in the last quarter.

to afford
To have enough money to be able to buy or treat oneself to something.
Dieses Jahr können wir uns endlich einen Urlaub am Meer leisten.
This year we can finally afford a vacation by the sea.

to provide / render
To give or render something specific to someone, such as help, a service, or resistance.
Die Sanitäter leisteten dem Verletzten sofort Erste Hilfe.
The paramedics immediately provided first aid to the injured person.

to allow oneself
To allow oneself a certain, often negative or unwise behavior.
So eine unüberlegte Bemerkung kann er sich in seiner Position nicht leisten.
In his position, he cannot allow himself such an ill-considered remark.

to keep company
To stay with someone so that this person is not alone.
Meine Oma ist allein, deshalb gehe ich oft hin, um ihr Gesellschaft zu leisten.
My grandma is alone, so I often go over to keep her company.
The verb 'leisten' (to perform/provide/afford) is closely connected to the noun 'die Leistung' (performance, achievement). 'Leisten' is the action that leads to a 'Leistung' (performance, achievement).
Der Sportler hat eine beeindruckende Leistung gezeigt.
The athlete delivered an impressive performance.
Pay attention to the case of the reflexive pronoun. 'Sich (Akkusativ) etwas leisten' means to buy or afford something. 'Sich (Dativ) etwas leisten' means to allow oneself negative behavior.
Ich leiste mir ein teures Abendessen. (kaufen)
I'm treating myself to an expensive dinner. (buy)
In the meaning of 'vollbringen' (to accomplish/perform), 'leisten' is often combined with abstract nouns that describe an effort. Typical examples are: 'Arbeit leisten' (to do work), 'einen Beitrag leisten' (to make a contribution), or 'Überstunden leisten' (to work overtime).
Viele Menschen leisten ehrenamtliche Arbeit in ihrer Freizeit.
Many people do volunteer work in their free time.
The structure for 'sich etwas leisten können' (to be able to afford something) is fixed: subject + können + sich (accusative) + object (accusative) + leisten. The reflexive pronoun 'sich' is obligatory here.
Ein neues Auto können wir uns im Moment nicht leisten.
We can't afford a new car at the moment.
When you give or render something to someone, the structure is: jemandem (dative) etwas (accusative) leisten. Common combinations are 'Hilfe leisten' (to provide help), 'Widerstand leisten' (to offer resistance), or 'einen Schwur leisten' (to swear an oath).
Die Nachbarn leisteten der Familie nach dem Brand schnelle Hilfe.
The neighbors provided quick help to the family after the fire.
The phrase 'jemandem Gesellschaft leisten' (to keep someone company) is a fixed combination. The person who should not be alone is always in the dative.
Ich besuche meinen Großvater, um ihm etwas Gesellschaft zu leisten.
I visit my grandfather to keep him a little company.
to give
Geben and leisten can both be associated with providing help. Hilfe geben is the general, neutral form, whereas Hilfe leisten emphasizes the support provided and often suggests an organized or more formal context. Geben is common in everyday situations; leisten is especially fitting for specific assistance.

Die Sanitäter leisten dem verletzten Kind sofort Hilfe.
The paramedics immediately provide help to the injured child.
Die Nachbarin gibt dem verletzten Kind sofort Hilfe.
The neighbor immediately gives the injured child help.