The phrase "call it a day" is a fairly commonly used idiom that means to leave or stop doing the current activity. Usually, it is used at the end of a workday or an otherwise strenuous activity to indicate that the day of hard work or play is finished and it is time to go home and relax for the evening, although this is not always the case. The phrase might also be used by someone at bedtime who wishes to stop the conversation or other evening activities and go to bed.
Common examples of usage of the phrase might be "I'm getting tired and dinner will be ready soon, so let's do one more hole of golf and then call it a day," or "I will be home soon; I am going to finish a few things up here at work and then call it a day." The phrase is typically used to express the action of quitting an activity rather than to refer to the activity itself as being finished. For example, it would be incorrect, although likely understandable, to say, "The basketball game was called a day because of the rain." Most people familiar with the idiom would probably understand the meaning of that sentence, though it is not correct and technically doesn't make sense. Idioms such as this one are often difficult to translate between languages, so for people just learning to speak English, it might be helpful to ask native English speakers if the usage is correct when using this phrase and other common idioms.
The phrase is relatively informal, but it would not be inappropriate to use in polite company. A boss might signal to his employees that they may go home by telling them to call it a day. Just as easily, two children exhausted from a day of playing outside might decide to call it a day.
A few other phrases similar to "call it a day" might be used in place of this idiom. "Call it a night" might be used in the evening or at nighttime to indicate that an activity should be put on hold for the night. "Call it quits" can be used in scenarios where quitting will be permanent, as opposed to simply for a break overnight or the weekend, though it is sometimes used in the same manner as "call it a day."