"Party Level" is the average level of the characters in a party. While most modules and campaigns say they are designed for parties of 3-5 characters, the DMG specifically states that monster Challenge Ratings (CR) is based on a party of four.
A single monster with a challenge rating equal to the adventurers' level is, by itself, a fair challenge for a group of four characters.(DMG p.274)
Thus, a 3rd level party, is a group of four 3rd level characters or some combination that averages to 3rd level. If your party has more or less characters than four, you can figure the party level by averaging as if there were four; ie divide the total levels by 4 instead of the actual number of characters.
For example: A party of six 3rd level characters, would have a total character level of 18; divided by 4 gives a party level of 4.5
This encounter calculator is built for 3.5e but it has a party level calculator.
For Princes of the Apocalypse, yes it assumes you have a party of four 3rd level characters. If you have 6 characters in your party then they would all be 2nd level to form a 3rd level party. However, six second level players might have difficulty in the harder encounters due to lower abilities. This module appears to be the third in a larger campaign. If you are running fresh characters, then just hand wave exp, and level them up to 3rd. Or, run them through a couple other modules first.