Three domains vs 5 Kingdoms

From my book:

In the older, five kingdom system of classification, all organisms are placed into one of five kingdoms.

In the new, three domain system all organisms are placed into one of three domains - large superkingdoms that are above the kingdoms in the taxonomic hierarchy.

Organisms that were in the kingdom Prokaryotae (unicellular organisms without a nucleus) are separated into two domains- the Archaea and Bacteria. Organisms from the other four kingdoms (organisms with cells that contain a nucleus) are placed in the third domain- Eukarya.

The Prokaryotae were reclassified into two domains because molecular phylogeny suggested that archaea and bacteria are more distantly related than originally thought.

And as ali242 pointed out, the older system was more physiologically based. The new system used molecular phylogeny which looks at actual molecules (DNA + Proteins) to see how closely related organisms are, e.g. more closely related organisms have more similar molecules.

Hope this helps!