Why do we need deep sequencing? Why cannot the sequencing technologies read all the nucleotides correctly at the first read? Sorry since this question is too trivial, I don't have a biological background at all, and I have just started doing research in CompBio. Thanks.
In a nutshell, DNA sequencing technology has a limit to how long a stretch of DNA it can read in one go.
So what most commonly occurs is the length of DNA you wish to sequence needs to be (almost randomly) chopped up into given lengths (depending on the technology) and each length or read is sequenced in parallel. But now you don't know which lengths to stick together! i.e. the ordering of these chopped up lengths. So you sequence it many times over (deeper) and this way you can align contiguous ends of these lengths together like a jigsaw puzzle. The more times you sequence the more accurately the 'contigs' will be aligned.
DNA Assembly Diagram
Comment if you want more details, but the technical term you want to google is "sequencing assembly".
Here's the wiki
Deep sequencing is naturally error prone. Sequencing will never be perfect, because no enzyme will ever perform 100.00000% perfectly.
In Illumina sequencing, you put your starting molecule down on the flowcell, then the polymerase makes a cluster of copies around it. But at each step of building each copy, there's a chance the polymerase will make a mistake. Then at sequencing, a single complementary labeled dideoxynucleotide is added to the complementary chain. But there is always a chance the enzyme will make a mistake. Then after the base is read, the label needs to be cleaved. Another step where the enzyme might make a mistake. Then the base is converted to deoxy, another possible error. Even if each step is very unlikely to fail, after a lot of steps, there will be enough problems that the cluster won't show the correct color uniformly. The software tries to compensate, but the result is that you will have reads with inaccuracies. That's why you have to have depth.
Another important point is that we almost always sequence a population of cells, not just a single cell. Cancer cell populations, for example, can have multiple sub-populations of cells with different genetics (subclones). Deep read sequencing allows us to see this heterogeneity, and also measure the abundance of each sub-clone. Even with a single cell, we can see the abundance of different alleles... Usually 50-50 in normal cells, but can get pretty crazy in cancer.