der Acker
field
A piece of land used for agriculture to grow plants such as grain or vegetables.
Im Frühling pflügt der Bauer seinen Acker.
In spring, the farmer plows his field.

field
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field
A piece of land used for agriculture to grow plants such as grain or vegetables.
Im Frühling pflügt der Bauer seinen Acker.
In spring, the farmer plows his field.

The noun 'der Acker' is closely related to the verb 'ackern'. 'Ackern' originally means to work a field, but colloquially it is also used for 'to work hard' or 'to slog away'.
Für diese Prüfung habe ich wirklich wochenlang geackert.
I really worked hard for weeks for this exam.
In an agricultural context, 'Acker' is often combined with typical verbs, such as 'einen Acker bestellen' (to cultivate a field), 'pflügen' (to plow), or 'säen' (to sow).
Nach der Ernte muss der Acker für das nächste Jahr gepflügt werden.
After the harvest, the field has to be plowed for the next year.
Using 'Acker' for a bad playing field is purely colloquial and has a negative, derogatory meaning. It is used to complain about the poor condition of the pitch.
Bei dem Regen verwandelt sich der Fußballplatz in einen echten Acker.
In this rain, the soccer field turns into a real muddy pitch.
place / space
'der Platz' and 'der Acker' can both refer to a larger outdoor area. In sports, 'Platz' is the neutral word for a field, court, or area used for an activity. 'Acker' actually means a field where plants are grown. Colloquially, however, a bad soccer field can be called an 'Acker' in a negative way if it is muddy or damaged. This can lead to confusion. For a normal playing field, say 'Platz'; 'Acker' only fits in agriculture or, jokingly and critically, for a very bad field.

Nach dem starken Regen sah der Fußballplatz aus wie ein Acker.
After the heavy rain, the soccer field looked like a muddy field.
Der Platz vor der Sporthalle ist heute für das Turnier reserviert.
The area in front of the sports hall is reserved for the tournament today.