PowerShell exists to create a more powerful shell than Command Prompt, a more capable language than VBScript, and an environment with built-in support for remote servers and code documentation. Since its introduction, Microsoft's have added support for PowerShell scripting to many of their core products.
This comment by Jeffrey Snover, one of the original designers of PowerShell, explains the ideas and intent behind the language, and why it was developed instead of porting something like Bash from a Unix environment.
PowerShell provides a vastly improved scripting environment for Windows compared to previous .bat and .vbs methods; it includes PowerShell ISE - an editor and debugging environment, on the language side it has easy support for using lists, hashtables and regular expressions for pattern matching, as an interactive shell it has tab completion for command parameters and interactive help via
Get-Help, and it can natively work with COM objects, WMI, registry values, call out to any .Net Framework method or library, and create and use modules written in PowerShell code.
Microsoft Software that supports PowerShell for management includes: Windows Server (and many roles and features - Active Directory, IIS, DNS Server), Exchange Server, SQL Server, SharePoint Server, Windows Azure, and Office 365 components. Here is a full list of PowerShell modules included in Windows Server 2012 and Windows 8.1.
First released in 2006 as a downloadable addition to Windows XP and Server 2003, PowerShell has been significantly upgraded in 2009 (v2) with the addition of remote execution of scripts, and in 2012 (v3) and 2014 (v4).