It doesn't mean you would load the same entry into two places into the table -- it means a particular entry can be loaded to either of two places in the table. The alternative where you can only map an entry to one place in the table is a direct mapped TLB.
The primary disadvantage of a direct-mapped TLB arises if you're copying from one part of memory to another, and (by whatever direct-mapping scheme the CPU uses) the translations for both have to be mapped to the same spot in the TLB. In this case, you end up re-loading the TLB entry every time, so the TLB is doing little or no good at all. By having a two-way set associative TLB, you can guarantee that any two entries can be in the TLB at the same time so (for example) a block move from point A to point B can't ruin your day -- but if you read from two areas, combine them, and write results to a third it could (if all three used translations that map map to the same set of TLB entries).
The shortcoming of having a multiway TLB (like any other multiway cache) is that you can't directly compute which position might hold a particular entry at a given time -- you basically search across the ways to find the right entry. For two-way, that's rarely a problem -- but four ways is typically about the useful limit; 8-way set associative (TLBs | caches) aren't common at all, partly because searching across 8 possible locations for the data starts to become excessive.