to detain, to entertain, to keep, to put by
畱 centers on holding something in place: detaining a person, keeping an object, or putting something aside for later. The entertain sense is a specific application of keeping a guest.
畱 is an older form of 留. The modern 留 is a simplification, while 畱 preserves a more complex upper component. The character likely combines 田 (field) with a phonetic element, but the exact historical development is uncertain.
The bottom 田 is a field, and the upper part looks like a complicated gate. Imagine detaining someone at the gate of a field, keeping them there.
For リュウ, think of a detainee named Ryu who is kept at the field gate: Ryu -> リュウ.