If I run DESeq(betaPrior=FALSE) I get two coefficients: the intercept (group A) and the difference between condition B versus A.

dds <- makeExampleDESeqDataSet()

res1 <- DESeq(dds, betaPrior = FALSE)
resultsNames(res1)
[1] "Intercept"        "condition_B_vs_A"

If I run DESeq(betaPrior=TRUE) I get an intercept plus an effect for each group. Here I do not know what the intercept represents, which is the question of this post.

res2 <- DESeq(dds, betaPrior = TRUE)
resultsNames(res2)
[1] "Intercept"  "conditionA" "conditionB"

Thanks in advance!

The intercept with betaPrior=TRUE (which is kind of the "old way" that DESeq2 did shrinkage) gives a middle point that the expected normalized counts for all groups are shrunk towards.