The Alu sequence, alternately referred to as the Alu element or simply Alu, is a sequence of about 300 base pairs that repeatedly appears tens of thousands of times throughout human DNA, but has uncertain function. It has, in the past, been lumped in with junk DNA, although it does appear to have useful functions including effects on aspects of polyadenylation, gene splicing, and RNA editing, and harmful functions in causing disease.
Alu is a type of transposable element, a sequence of DNA that can sometimes copy and paste itself from one segment of DNA to another. It is perhaps worth noting that while Alu is remarkable in humans, it is officially a SINE (Short Interspersed Element), rather than a LINE (Long Interspersed Element), as it is less than 500 base pairs long. Alu is common in mammals and is one of the most common transferable elements in humans, but is not particularly exceptional in the context of eukaryotic genomes as a whole.
It appears that Alu is important enough that evolutionary pressure will select for and against it, with these elements slowly collecting in gene-rich segments of our DNA over time. It is interesting to note that another common transposable element in humans, LINE1, is selected against in gene-rich regions, so there is something special about Alu. Alu and related elements (often referred to as the Alu family) make up about 5% of the human genome.
Uncertain function does not mean uncertain usefulness, however. It is estimated that a new Alu element appears in humans about once every 20 births, and they appear in random spots across the genome. This means that they can be used to track genealogy; an shared placement of a Alu segment strongly suggests shared ancestry.
While many transposable elements are also useful over longer timelines -- we can compare the number of LINE1 shared between us and other great apes to estimate when our lineages split, for example -- Alu is not useful in this way. For reasons unclear, humans have gathered more Alu repetitions in our genomes than other mammals have.
Alu sequences are believed to be the source of many human genes, either through mutation or exonization, and appear to have effects on gene expression, RNA editing, and estrogen receptors. While we are still finding out what diseases are most often caused by Alu transpositions, it appears that some cancers and Friedreich's ataxia are caused by Alu popping up in the wrong places.