Line count in ABAP programming tell us how many lines the report can have.
SYNTAX: REPORT <rep> LINE-COUNT <length>[(<n>)].Here <length> will decide the length of complete report or list length. If this is 0 then complete window will be considered(standard length). If you mention <n> then besides output list, the report will store <n> lines for footer. If nothing is in footer, then only empty line will display.
To understand better, go to se38 and create the below simple report.
REPORT ztest_first_report LINE-SIZE 40 LINE-COUNT 4(1).
WRITE: 'SY-LINCT:', sy-linct.
SKIP.
DO 4 TIMES.
WRITE / sy-index.
ENDDO.
Execute:

Here total 5 pages created. We have mentioned in our line count as 4(1) . Means report can have max 4 lines in one page, where 1 line is reserved for footer.
Now let's increase the length from 4 to 5.
REPORT ztest_first_report LINE-SIZE 40 LINE-COUNT 5(1).

Now each page can hold 5 lines with 1 line as footer.