The long pole is the part of the project that is on the critical path due to its length. For example, if you have a project that consists of three independent sub-projects, then the sub-project with the longest completion date is the long pole.

The etymology of this term is simultaneously obvious yet hard to pin down. Intuitively, the long pole is the one that determines the height: If you have a tent supported by three poles, then the long pole decides how tall the tent is. If you have a collection of poles you want to put in the back of a pick-up truck, the long pole is the one that decides how big a bed you need. If you have a set of poles and you hold them in your hand in a sheaf and rest the bottoms on the ground, then the long pole is the one that sticks up the highest.

It is my impression that the tent analogy is the one that provides the source for this bit of Microspeak, but I'm not absolutely sure. If true, it's a nice bit of double-wordplay, because not only is it an analogy, but it's also a pun: The long pole is the one holding everything up.

You don't want to be a long pole in your project, because that just means that everybody will be giving your component extra scrutiny to make sure it's not going to make everything late.

Here are some citations.

Design on track, but setup work appears to be long pole.
XYZ work is long pole in the schedule; not clear whether issue can be mitigated.
XYZ is still the long pole, now out [i.e., over schedule] by about six days, down from eight days last week after the ABC work was offloaded to UVW.