Hashem is a word used to refer to God by many people of the Jewish faith. Literally translated, the name means simply, “the Name.” It is used commonly to replace the name Adonai in casual speech.
The name of God is a serious topic in Judaism, and there are many rules and traditions surrounding its use. It is forbidden to speak the four letter name of God, YHWH, also known as the Tetragrammaton. Only the High Priest may speak this name, and then only in the Temple — which, of course, no longer exists, making it prohibited for anyone to speak the name anywhere.
Since it is necessary to speak the name of God during certain prayers, a way had to be conceived of to refer to Him without committing blasphemy. So it is that when reading prayers which refer to YHWH, most will read the name Adonai, instead. Adonai means simply Lord, and it is not considered blasphemous to speak this name.
There is a principle in Jewish law that seeks to set out further limitations in order to reduce the chance of a serious law being broken. Since the prohibition against blasphemy is so serious, it is important that there exists a further level of protection to avoid using the Tetragrammaton. The name Hashem is therefore used as a substitution for Adonai in situations outside of prayer.
The use of this name, a more generic word, therefore further reduces the chance that one may inadvertently pronounce the forbidden name of God. It also limits frivolous uses of Adonai, keeping that term more sanctified and special. This helps show a respect for the use of God’s name, and is often used for other terms given to God in addition to Adonai, such as Elohim or Shaddai.
Depending on the person, the use of Hashem may be more or less frequent. Some people have no objection to using names such as Adonai or Elohim in everyday speech, and so Hashem becomes simply another name. Others would absolutely never use these names in anything but actual ritual prayer, and so it is a cornerstone of the ability to discuss God in more general contexts. Even in many recordings of prayers, some will replace terms such as Adonai, as a recording will likely be played back many times outside of the proper ritual context.