The dagesh is a dot which is drawn inside a Hebrew letter to
modify its sound.
Though it's possible to add a dagesh to any letter, contemporary Hebrew only seems to use it for the letters bet ב, kaf כ & ך, and pe פ & ף.
The effect of the dagesh on the above letters is to turn a fricative sound into its equivelant plosive:
In computer typography there are two ways to use a dagesh with Hebrew text. Here are Unicode examples:
bet + dagesh: בּ בּ kaf + dagesh: כּ כּ pe + dagesh: פּ פּ
bet with dagesh: בּ בּ kaf with dagesh: כּ כּ pe with dagesh: פּ פּ
This article currently only concerns the use of the dagesh in modern, Israeli Hebrew. Gritchka has sent me many notes on the use of the dagesh in Biblical Hebrew which I hope to incorporate.
Lonely Planet Hebrew Phrasebook