There are two types of label retention mode: Liberal and Conservative. In liberal mode, every label sent by every LSR is stored in the LIB. In conservative mode, only the label that was sent by the best next hop (determined by the IGP metric) for that particular FEC is stored in the LIB. In the diagram below, you can see that R1 will receive two labels about the 10.1.1.1/32 network. These are labels 20, from R3, and label 21 from R2. Lets decide that R1 is using liberal retention to store these labels. So R1 will store both of these labels in the LIB. If the IGP was OSPF and the link via R3 had the lowest cost, then the next hop to this network would be via R3. So label 20 would be used in the LFIB (i.e. the data plane to forward packets to this destination). The end result is that R1 will have label 20 and 21 in the LIB, but only label 20 in the LFIB.
Lets say that R1 is actually now using conservative mode. He will, again, receive label 20 from R3 & label 21 from R2. However, because the best next hop is via R3 (lowest cost), it will discard label 21. The result is that R1 will store label 20 in the LIB, and label 20 in the LFIB.
As always, with most things in networks, there are benefits and drawbacks of both modes. In liberal mode, the convergence is quicker in the event of a failed link. In the network above, if the link between R1 and R3 failed, then R1 will already have another label for this FEC in the LIB (label 21 from R2). So the IGP will re-converge, the LFIB will delete the entry using label 20, and use Label 21 via R2 instead. The drawback of liberal retention is that an enterprise network may have many redundant paths around the network for each FEC. So the LIB can take up a lot of memory.
The benefit of conservative mode is that it uses less memory. But the drawback is that convergence is slower in the event of a link failure because no backup entry exists in the LIB.