Right from the man page you reference:
elf - format of Executable and Linking Format (ELF) files
ELF defines the binary format of executable files used by Linux. When you invoke an executable, the OS must know how to load the executable into memory properly, how to resolve dynamic library dependencies and then where to jump into the loaded executable to start executing it. The ELF format provides this information. ELF magic is used to identify ELF files and is merely the very first few bytes of a file:
% od -c -N 16 /bin/ls 0000000 177 E L F 002 001 001 \0 \0 \0 \0 \0 \0 \0 \0 \0 0000020
or
% readelf -h /bin/ls | grep Magic Magic: 7f 45 4c 46 02 01 01 00 00 00 00 00 00 00 00 00
These 16 bytes unambiguously identify a file as an ELF executable. Many file formats have "magic" bytes that accomplish the same task -- identifying a type of file.