Which version of LW are you using?

Maybe the host that you were downloading from went offline before your download finished. If you're waiting in line then you're in a queue for that download & have to wait until the host has a free upload slot (so that you can download).
Sometimes you just have to be patient. But if downloads are taking too long to resume, you can start a new search for the file... sometimes that will kickstart a stuck download. Other times it might just be quicker to kill the current download, search again & download from a different host.

If you're new to LW, start off by reading the FAQ & User Guide below (click on links).
Frequently Asked Questions - LimeWire
LW 5 FAQ - LimeWire
User Guide - LimeWire

Other useful links, with heaps of helpful info, are below
Fake files showing up in search results

How to use Bitzi

WARNING: Viruses on the network you should be aware of

HOT Topics Quicklist for problems getting started with LimeWire