The effective length for a transcript is the essentially the number of possible start positions for a read or fragment within that transcript, given that the read or fragment must fit entirely within the transcript boundaries. So if you have a transcript of length L and all of your fragments are of length F, then the effective length of that transcript is
L - F + 1
Things are complicated by the fact that in an RNA-Seq experiment, the fragments have varying lengths, so the effective length is actually the *mean* number of possible start positions for a fragment within a given transcript. This changes the formula to something like
L - mean(F) + 1
The exact formula is slightly more complicated to take into account situations in which some possible fragment lengths are longer than the transcript itself, but for relatively long transcripts this formula is correct.
At the gene level, RSEM considers the effective length of a gene to be the abundance-weighted mean effective length of its isoforms.
The effective count for a transcript is RSEM’s estimate of how many reads/fragments truly map to that transcript. It essentially includes all reads/fragments that uniquely to that transcript, along with some estimated fraction of the reads/fragments map non-uniquely to that transcript.