I'm trying to understand what exprs() function does to an AffyBatch Object. I would expect to get a matrix with a row for every gene/probeset and a column for every sample. 

> library(affydata) 
> data(Dilution)
> Dilution
AffyBatch object
size of arrays=640x640 features (35221 kb)
cdf=HG_U95Av2 (12625 affyids)
number of samples=4
number of genes=12625
annotation=hgu95av2
notes=
> head(exprs(Dilution))
     20A   20B    10A   10B
1  149.0 112.0  129.0  60.0
2 1153.5 575.3 1262.3 564.8
3  142.0  98.0  128.0  56.0
4 1051.0 597.0 1269.0 570.0
5   91.0  77.0   90.0  46.0
6  136.0 133.0  117.0  62.0
> dim(exprs(Dilution))
[1] 409600      4

As you can see, I get a matrix of 409600 rows, instead of 12625 (the number of genes).

I don't understand what the rows of this matrix represent. Do they represent probe cells?

Thank you.

EDIT: I've just noticed that 640*640=409600. Anyway, I still don't understand what these numbers represent.

Affymetrix arrays all have multiple probes (25-mers) that interrogate a single transcript. The array you are looking at used primarily 16 probes per probeset (e.g., there are 16 25-mers that are intended to interrogate a particular transcript. Each 25-mer is called a probe, and the set of probes for a given transcript is a probeset).

The numbers represent the partially processed intensity values for each probe, and aren't particularly useful by themselves. If you run rma on those values, you will get the background corrected, normalized, summarized values for each probeset, which you can then use to compare gene expression between samples.

There are any number of articles, white papers, vignettes, etc that describe the Affy platform and how to analyze the data. One useful paper you could read is the citation for the affy package:

 Gautier, L., Cope, L., Bolstad, B. M., and Irizarry, R. A. 2004.
  affy---analysis of Affymetrix GeneChip data at the probe level.
  Bioinformatics 20, 3 (Feb. 2004), 307-315.