Download Mesh (also referred to as the Alternate-Sources Mesh)
Sources for a file (ie. other users on the network) may retain a list of sources from which they obtained the file, and partial downloaders will certainly have such a list. Each of those sources has their own list of further sources for that file and this distributed set of lists is the Download Mesh.
When you successfully contact a source, they will pass you the sources on their list so that your Shareaza may attempt to download from them as well. This is the case even when the source is busy, so at least some benefit is obtained from the connection.
Many sources are on dial-up modems with arbitrary cut-offs (eg. every two-hours) and get assigned temporary IP addresses. Their presence in the meshes is a disadvantage because once they have redialled, their previous IP address is worthless. Your Shareaza will attempt to connect to all of these but will eventually drop them from its own list - unless you set the Advanced Setting Downloads.NeverDrop to 1 (true). True for this option will mean that these useless sources are retained. (But there are good reasons for setting it to true - if you have only one source for a file or set of files and they are only online sporadically then you really don't want Shareaza to throw away their IP address!!).)
(Another reason for setting NeverDrop is that some users have very large libraries and are very popular - it takes much patience to get files from them and they will be busy enough that Shareaza thinks they are no good. It's shame that Shareaza doesn't have per-source control of this.)