The Danish word lægdsrulle means military levying roll.
Danish military records are not the easiest records to research, but if you take your time to get to know them, you will see that they are an invaluable source for genealogists. For instance, I often use information from military levying rolls as part of the evidence for identifying a man who emigrated from Denmark because it was typically noted in the rolls when a person emigrated and whereto.
I have written several blog posts about Danish military records, especially military levying records. Hopefully, they can help you understand the records and their uses:
The Earliest Military Levying Rolls from about 1788
Military Levying Rolls by Local and National Authorities
Following a Person from One Military Levying Roll to Another
Military Levying Rolls as Substitutes for Lost Church Books
Annotations in an 1818 Military Levying Roll
Researching 20th Century Military Levying Rolls
Military Case Files in County Collections
The image at the top: N.P. Nielsen, photographer, Gothersgade, Copenhagen, photograph of a soldier, unddated; imaged from original filed in Juhl-Hansen Collection; privately held by Lene Dræby Kottal, Odense, Denmark (2022). The soldier is probably Thomas Jensen Juhl (1918-1971), who was the brother of Lene Dræby Kottal's grandmother Jenny Kristine Juhl (1921-2008). Jenny left behind the photo in her collection. The photographer died in 1948, wherefore the photo is free of copyright.