Draw doesn't actually mimic anything in Microsoft's Office lineup. Despite the name, it's less Microsoft Paint and more of a tool for designing flow charts and the like: shapes you create instantly become adjustable, which should prove invaluable for quickly sketching out a diagram to toss into a document or Impress slideshow.
Math is a formula editor, which you can use to create mathematical formulas -- it's akin to Microsoft's Word Equation Editor. I'll admit that I'm well out of my element here, but the app lets you build rather complex-looking formulas by typing right into a dialog box and following the proper syntax. I generally meandered about the standalone app, but you can also use it to insert formulas directly into the other LibreOffice apps, which I suspect will be more useful.
And finally, there's Base -- LibreOffice's answer to Microsoft Access. I'm well out of my wheelhouse here, but the databases you create in Base can complement the rest of the apps LibreOffice suite, as well as being used on their own.
Stuck in the past
LibreOffice is an excellent Microsoft Office alternative that'll do just about everything you need it to, quickly and efficiently. And in a world without I wouldn't think twice about recommending it. But while LibreOffice has championed mimicking and even one-upping Microsoft's apps, the competition was busy marching ahead, developing tools to address the new ways we get to work. The most crucial of these is cross-device support.
Yes, LibreOffice will work on your Windows, Mac or Linux machine. But an increasing number of us are toting iOS and Android tablets about, and a lightweight device with great battery life is a tantalizing prospect when I need to hammer some words out but don't want to lug around a proper laptop.
I generally turn to Google Docs on my iPad, which wraps editing and cloud-syncing into one neat package. But there are plenty of other alternatives in this brave new world of office suites -- including an Android version of LibreOffice is in development, and you can even grab an experimental daily build if you're feeling adventurous. But there's currently no timetable for when we could expect a release.. They work wherever we do, and offer functional, accessible interfaces and cloud-syncing through services like Dropbox. Some of them -- including WPS Office -- are even free. The Document Foundation project's wiki page states that
LibreOffice (and OpenOffice, the open-source project from which it forked) was the gold standard in free Microsoft Office alternatives for quite some time. But while new competitors crept out of the woodwork and old stalwarts like Microsoft retooled their offerings, LibreOffice just kept on chugging along in the same myopic direction.
Speed and compatibility are lofty goals to aim for, but a feature list and user interface that's frozen in time is detrimental in an era where new free options are doing a great job in the compatibility department, and powerful features that work around our increasingly mobile lives -- they look nicer, too. Until LibreOffice steps into the present and offers more, it'll remain adrift in a sea of increasingly better options.