Min. profile is a small and basic root filesystem contains busybox, imx test, imx lib, etc. The building time is short around 30mins.
FSL gnome profile is a GNOME GUI example. It contains many packages and it will start a GNOME GUI when the board start up. The building time is very long ~4-5hrs.
You can compare the .profile files of each profile under <ltib>/config/platform/imx/.
e.g. min.profile is Min. profile, release_gnome.profile is GNOME profile.
After you selected the profile, you can select/deselect the package again in the "Package List" in LTIB configuration.