To express that the eukaryotes have large genomes, one must certanly be comparing them to organisms with much smaller genomes, the prokaryotes. It’s the analysis between these organisms which will give conclusive evidence as to the reasons the eukaryotes have large genomes.
Immediately one jumps to the idea that the eukaryotes tend to be more complex and therefore they should have a bigger genome, where would inevitably produce more genes. This is obviously true, though the complexity of the genome doesn’t directly correspond to an increase in genome size. Wheat features a far larger genome than ours however, you might hesitate to call them more complex. Therefore, there has to be more subtle underlying reasons why the eukaryotes have such large genomes.
Transposable elements enhance the size of genomes by copying and inserting into different parts of the genome. However, transposable elements also occur in the prokaryotes and the affect of the transposons on eukaryotes in increasing the size of the Genom genome is probably negligible. One reasons why the affect of transposons isn’t always detrimental to the organism is due to the introns within a eukaryote. The gene rich DNA of the prokaryotes is in sharp contrast to genes scattered around eukaryotic genomes. The introns in the eukaryotic genome cause them to become much, much larger than in the prokaryotes. The gene number difference in eukaryotes is about 10 fold whereas the base pair number may be 1000 fold bigger. The question therefore lies within the introns of the eukaryotes. Why are there so many introns in the eukaryotic genome; giving rise to its ‘large size’?
Since the eukaryotes evolved from the prokaryotes one must elucidate the purpose of the introns in the eukaryotes as, say a stream (against transposons, mutation etc). However, this is also construed to have the same equally beneficial properties in prokaryotes. A much better approach is always to analyse the energy output. Prokaryotes use 25% of their energy production in DNA copying and maintenance (the other 75% being that of protein production). Therefore, any upsurge in size of the DNA in prokaryotes would be too costly for the organisms to keep and replicate and thus the DNA is stripped down to a very gene rich molecule. Eukaryotes are profligate in pouring energy within their genomes (due to their greater energy production capacity as an immediate consequence of experiencing specific organelles devoted to the purpose) and as a result they can afford to be so disgracefully inefficient and allow accumulation of introns.
Another and probably the main consequence of to be able to pour large amounts of energy in to the genome is that eukaryotes can allow gene duplication events, which produce proteins that differ very slightly. Not merely this, in plants especially, entire duplication of genomes and addition of different divergent genomes are commonplace within that kingdom. Giving these organisms such huge genomes.