The biggest difference between toothed and baleen whales is the way they feed. Where toothed whales hunt for fish, squid or other larger prey (which they can catch and tear apart with their teeth) do baleen whales feed on much smaller prey. It is always a strange thought that the largest animals who have ever lived on this planet are feeding on one of the smallest: several species of zooplankton. They take huge gulps of water in their mouth and then press out the water through their baleen plates that work as a big sieve, filtering the small animals from the water.
At first sight this might sound strange, but come to think about it it does make sense. Only about 10% of the biomass of the first stage will make it to biomass of the second part of the food chain. The rest is either not digested, used for energy or lost in other ways. The longer the food chain, the more food is needed at the base to sustain the animals at the top. By making sure the food chain is very short (only phytoplankton – zooplankton – baleen whales), there is far less biomass lost over the different steps, so the whales can grow larger.