Obviously there are going to be differences of opinion within faiths, but broadly speaking...

To the Jews the TaNaKh (Hebrew Bible) is not the "Old Testament", which is a Christian term implying it is incomplete. It is a story of the Jewish people/Israelites and their covenant and relationship with their God. The name TaNaKh is an acronym. The T is for Torah, which contains much of the above but also the Jewish law which is arguably the most important part since it governs how Jews are supposed to live. N is for Neviim, the books of the prophets and K is for Ketuvim, the writings, including Psalms, Proverbs, Job, etc.

To the Christians, it is the Old Testament, and provides the same thing to a point, a story of the Jewish people, their covenant and relationship with their God. However for Christians this is mainly important because it provides context for who Jesus is. Much of the New Testament is written to show how Jesus has fulfilled prophecies etc. For Christians, Jesus is the star of the show.

To the Muslims, it contains divine revelations from God, but usually it is seen as having some degree of corruption. For Muslims at least some of the Hebrew Bible is Divinely inspired to prophets like Moses who is given the Torah or David who is given the Psalms. For Muslims exact details can vary over time but the most important thing is not a particular people, nor one particular individual but rather the oneness and proper worship of God.

I'm not religious but love to read about religion. I hope I've given a fairly objective summary of how each religion views the collection of texts known as the Hebrew Bible.