At their heart, DVDs are merely carriers of data files with compressed audio-visual information contained therein. This information can be placed on DVD in one of two resolutions; 720 x 576 pixels (PAL DVDs), or 720 x 480 pixels (NTSC DVDs), and with various frame rates (24, 25, and 30 frames per second are common). The DVD player itself takes this data file and formats it appropriately for display in either PAL or NTSC.
In principle, PAL DVDs have a compelling advantage over NTSC DVDs. PAL DVDs have 576 pixels of vertical resolution versus 480 pixels of vertical resolution. That's a 20% increase in resolution for a PAL DVD as compared to an NTSC DVD. Increased resolution translates into a better looking image. However, this is an overly simplistic way of looking at the whole PAL vs NTSC issue as there are other factors that need to be taken into account.
Basically PAL - UK/Europe video mode. Displays picture in full colour and fits to screen for PAL TVs.
NTSC - US/etc. - Displays full colour and fits to screen for NTSC TVs. Different regions use different modes. And if you try playing an NTSC DVD/Game on a PAL machine, it either will refuse to play, or play in black in white, possibly not fitting to screen and piossibly flickering (never experienced, but I hear about it)
If you have a "region free" TV though it's a different matter. Both formats will play fine.