to cheer on / to stoke / to incite
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to cheer on
To encourage and support someone through shouts and applause, especially in sports.
Die Fans feuerten ihre Mannschaft bis zur letzten Minute lautstark an.
The fans loudly cheered on their team until the final minute.
'Anfeuern' (to cheer on / to stoke / to incite) is a separable verb. The prefix 'an-' stands at the end of the sentence in main clauses. The basic idea of 'Feuer' (fire, energy, passion) appears in all meanings.
Ich feuere dich bei deinem Marathon an!
I'll cheer you on during your marathon!
As a separable verb, 'anfeuern' (to cheer on / to stoke / to incite) changes its form depending on the sentence type. In a main clause it separates, in a subordinate clause it stays together, and in the infinitive with 'zu', 'zu' goes in the middle.
Der Trainer feuerte seine Spieler an.
The coach cheered his players on.
You can recognize the meaning from the object: If you 'anfeuern' (cheer on) a person or team, it means 'ermutigen' (to encourage). If you 'anfeuern' (stoke) a fire or stove, it means 'entzünden' (to light). If you 'anfeuern' (incite) someone to do something, it means 'anspornen' (to spur on).
Die Zuschauer feuerten den Läufer auf der letzten Runde an.
The spectators cheered on the runner during the final lap.
In the meaning 'anspornen/anstacheln' (to spur on/to incite), the preposition 'zu' is often used to name the action someone is encouraged to do. The structure is: 'jemanden zu etwas anfeuern' (to incite someone to do something).
Die Menge feuerte den Redner zu noch radikaleren Aussagen an.
The crowd incited the speaker to make even more radical statements.
to extinguish / delete
'löschen' and 'anfeuern' form an opposite pair when talking about fire. You use 'löschen' when a fire should stop burning. You use 'anfeuern' when you light a fire or make it burn more strongly. So the difference is the direction: with 'löschen', the fire becomes weaker or goes out; with 'anfeuern', it becomes stronger.
Hannah feuert den Ofen mit trockenem Holz an.
Hannah stokes the stove with dry wood.
Nach dem Grillen lösche ich die Kohlen mit Wasser.
After grilling, I put out the coals with water.