No arguments with the advice you've been given so a far.
Here is a thread where someone asked a similar question, and there were several responses that expanded on the possibilities. This may be of some help to you -
http://www.avforums.com/forums/speakers/1670699-external-tv-speakers-amp.html
The Headphone out is the least of the options, but it is also the simplest, and cheapest. For someone who simply want better sound than the build-in speaker, which get worse very year with new models, then some type of Active Speaker, meaning speakers with built-in amps.
Again, you need to think long and hard about your real needs. Something like the
Onkyo HTX 22HDX could be a good choice for someone with basic simple needs, and it can be expanded to a full 5.1 with an upgrade kit, but they cost is roughly £300 (±£50).
Also, to give an helpful advice, we need a
working budget. The range is far too wide for use to be left guessing.
It is also helpful for us to know SPECIFICALLY what TV you have (Brand & Model). We can then look it up on-line and determine precisely what outputs are available. In the other thread, linked above, I explain the three main Output options on TVs.
In you want simplicity, minimal cost, least hassle with the best results, then Active speakers connected to the Headphone out is quick and simple. Though not necessarily the best.
How far you want to take it, and how far you want us to take it, is going to depend on your Budget.
Steve/bluewizard