The search page can be used (unsurprisingly) to search your account for messages matching particular criteria. The left folder list (assuming you are using IMAP) specifies which folders will be searched. Multiple folders can be selected by holding CTRL and selecting (Windows, other operating systems may vary). The search criteria are all ANDed; an OR based search is not currently possible. This means that only messages matching ALL the search criteria you supply will be found. Assuming you have a capable browser, there will be a button next to the Received On/Before/Since date selectors which will popup a calendar, to make date selection easier.
Once viewing the search results, they will remain until you navigate to a different folder.
Note: Some IMAP servers require that an emails' body be separated from the headers by the line ending sequence CRLFCRLF. Some Unix mailers however may well deliver an email with the body separated using LFLF. This may cause the IMAP server not to function as expected when performing body searches.