jemanden verständigen
to notify someone
To inform or notify someone about something, often in an urgent matter.
Bitte verständigen Sie im Brandfall sofort die Feuerwehr.
In the event of a fire, please notify the fire department immediately.

to notify / communicate / agree
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to notify someone
To inform or notify someone about something, often in an urgent matter.
Bitte verständigen Sie im Brandfall sofort die Feuerwehr.
In the event of a fire, please notify the fire department immediately.

The verb 'verständigen' is closely connected to words related to understanding. These include 'der Verstand' (intellect), 'das Verständnis' (ability to understand/understanding), and 'verständlich' (easy to understand).
Seine Erklärung war für alle gut verständlich.
His explanation was easy for everyone to understand.
The three main meanings have different sentence patterns. Informing someone: 'jemanden (Akk) verständigen' (to notify someone). Communicating: 'sich (mit jemandem) verständigen' (to communicate with someone). Reaching agreement: 'sich auf etwas (Akk) verständigen' (to agree on something).
Er verständigte sofort den Hausmeister.
He immediately notified the building manager.
In the meaning 'inform', the verb is often used for emergencies or urgent messages. Typical objects are 'die Polizei' (the police), 'die Feuerwehr' (the fire department), 'den Notarzt' (the emergency doctor/paramedic), or 'die Angehörigen' (the relatives).
Die Zeugen des Unfalls verständigten sofort die Polizei.
The witnesses to the accident immediately notified the police.
When it is about communication, the verb is reflexive. The language or method is given with 'in' or 'auf' (+ dative), and the communication partner with 'mit' (+ dative).
Obwohl sie verschiedene Sprachen sprachen, konnten sie sich irgendwie verständigen.
Although they spoke different languages, they were somehow able to communicate.
to understand
'verstehen' and 'verständigen' can both have to do with communication, but they do not mean the same thing. 'verstehen' describes grasping the sense of words, information, or an explanation. It can also mean that you can hear someone acoustically. 'sich verständigen' means that people communicate with each other and make themselves understood, even when it is difficult. 'jemanden verständigen', on the other hand, means to notify someone, often in an urgent situation. Learners easily confuse the words because both are connected to 'verständlich' (understandable). Pay attention to the direction: Ich verstehe etwas (I understand something); ich verständige jemanden (I notify someone) or ich verständige mich mit jemandem (I communicate with someone).

Nach dem Unfall verständigt der Fahrer sofort die Polizei.
After the accident, the driver immediately notifies the police.
Im lauten Zug verstehe ich den Durchruf kaum.
On the noisy train, I can hardly hear the announcement.