The primary benefit depends on what other browser you currently (or used to) use. IE (Microsft's internet Explorer) is still the most used 9because they gave it to everyone who installed Windows). Firefox is next and Opera is a very low third.
One main benefit can be memory use. If you open any other browser and also Chrome, Chrome will let you check how much memory each browser is using. First, find any page that uses a reasonable amount of memory - for example, gmail. Open up the same page simultaneously in each of (all) of the browsers you want to compare. Then, on the Chrome browser, right mouse click on any part of the blue edge of the browser window. Select Task Manager, then click on "stats for nerds" (bottom left). The resulting window will show you how much memory you are using for each web page you have open (so it's easier to compare if you have as few open pages as possible). You don't need to understand much about the results - all you need to know is that small numbers mean you are using less memory.
Chrome will beat everything. However, Chrome is especially good at beating Firefox for memory use (I find that Chrome uses only half the memory that Firefox needs for some of my most memory-hungry web pages). Chrome is not always much faster than Firefox but it is often faster than IE and other browsers. The times taken to download the initial product or updates are also much better than for other browsers, because chrome is so small.
Of course none of these are really the main reasons to switch to Chrome. Chrome has been created specifically so as to change the way we use applications. Currently we all buy an application, suffer the need to install it (often a nightmare) and then suffer further cost to upgrade it (frequently - that's what the manufacturers want!). All that should disappear. Instead, we will look for web-based applications. For example, Google Calendar, Google Docs etc. (I chose Google applications as examples because they're the ones I know). These exist on the web, are free to use and you just open them in your browser to use them. Take Google Docs (go to Google, select More.... and then select Docs) - it replaces Microsoft Word (which costs a fortune). Google Docs will open any Word document and will let you save documents in Microsoft Word format. You can of course edit in Google Docs. If you want you can even abandon Word and create and maintain your docs in Google Docs. So think about it, would you like to pay for your apps or get them for free? Google Chrome is designed to access the web-based services, which are currently often free or cheap and - in any case, they prevent you having to worry about maintaining the software!
In the end, so called "Open Source" programmers will expand their offerings and wite things that work in a browser, for free use. There's already lots of Open Source (for example, OpenOffice is free and replaces just about all the Microsoft tools that most of us use like Word, Excel, Powerpoint, etc.) but it's yet to work from within browsers. When they do, it's thought that they'll eventually kill off similar offerings from Microsoft (and others).
So longer term, what Chrome does is force all software manufacturers to think about writing browser-based applications, so JavaScript suddenly becomes a perfect tool to create applications. Browsers that don't run JavaScript correctly will lose out as Chrome does.
Of course, once tools (applications) become web-based, so browser-based, they will run on any operating system so the same service (the same version of the same software) will run on an Apple mac or a Windows Laptop or a Unix PC or any type of mobile phone, etc.
So all the big benefits will come soon but there's good enough reason to switch to Chrome now. remember though, Chrome is still in Beta test so it would be unfair to criticise it - we're still waiting for the full first release.
One last comment. Chrome works, even as a beta test version and it isn't even a Version 1.0 yet. Try to think of a single version of ANY Microsoft product that ever worked properly even as a fully released V1.0. (Clue, there has never been one.) Google is out to kill Microsoft and all it has to do is achieve quality - which it is successfully doing.
Chrome is worth getting used to. It's the future, a massive change in how we will work, even though it's mostly not obvious yet.
Cheers.