sich einigen
to agree
To come to a mutual agreement or compromise after a discussion or negotiation.
Die beiden Parteien konnten sich schließlich auf einen Preis einigen.
The two parties were finally able to agree on a price.

to agree / unite
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to agree
To come to a mutual agreement or compromise after a discussion or negotiation.
Die beiden Parteien konnten sich schließlich auf einen Preis einigen.
The two parties were finally able to agree on a price.

The most common use is reflexive: 'sich einigen' (to agree) means to reach an agreement. The rarer, non-reflexive form 'jemanden einigen' (to unite someone) means to bring different groups together.
Die Geschwister konnten sich nicht einigen, wer das Auto bekommt.
The siblings could not agree on who would get the car.
The verb 'einigen' (to agree/unite) comes from the number word 'eins' (one). The basic idea is to make 'one' unit or 'one' agreement out of several parts or opinions.
Nach langer Diskussion waren sie sich endlich einig.
After a long discussion, they finally agreed.
When you want to say what people agree on, use the preposition 'auf' followed by the accusative.
Die Koalitionspartner haben sich auf ein neues Gesetz geeinigt.
The coalition partners agreed on a new law.
to connect / to bandage
'verbinden' and 'einigen' can both describe people or groups coming together. 'sich verbinden' means to join together in order to pursue a shared goal. 'sich einigen', on the other hand, usually means to come to a shared decision after a discussion or disagreement. 'einigen' can also mean to bring different groups together into one unit. Learners may confuse the words because both are about togetherness. If the focus is on an agreement, 'sich einigen' fits; if the focus is on joining forces, 'sich verbinden' is more likely to fit.

Nach langer Diskussion einigen sich die Nachbarn auf einen neuen Termin.
After a long discussion, the neighbors agree on a new date.
Mehrere kleine Gruppen verbinden sich, um das Umweltprojekt zu unterstützen.
Several small groups unite to support the environmental project.