i'm installing slack on my usb drive. when installing lilo, i'm asked if i want to install on the mbr of my first drive. by first drive, does it mean the first hard drive i selected (being /dev/sdb)? or the first first drive (i.e. /dev/sda, which is my laptop)?

Is the installation for that laptop or is it portable?
If it is the first, then to the laptop disk.
If it is the second, then the usb disk.
Be sure not to set slackware as the native boot environment and reset the timer to 10 seconds.

To be more exact, "first drive" refers to the first hard disk in the BIOS boot sequence of drives. The BIOS assigns hexadecimal drive identifiers like this.

80 - First hard disk drive
81 - Second hard disk drive
82 - Third hard disk drive
83 - Fourth hard disk drive

When installing LILO from Linux, LILO has to figure out the BIOS drive ID associated with any device name that you provide. The "first" hard disk drive may change if you attach a new drive (including USB). Look in your BIOS to see the order it lists the drives in the boot sequence. If you change the order drives are checked for booting then the first drive or others may change. You may have to reinstall LILO.

The BIOS only knows about hard disk drives such as "hda" and not partitions such as "hda1". Because of that LILO has to save information about the sector offset location for files that it needs to get LILO started.

Linux may assign any device name to the "first hard disk drive" depending on how the BIOS assigns drive IDs to drives. The first hard disk drive isn't necessarily the one that was booted by the BIOS, but it is usually the first hard disk that the BIOS tries to boot.

Sometimes LILO gets the drive IDs wrong and there are LILO options to specify the exact relationship between Linux devices and BIOS drive IDs.

disk=/dev/sda
bios=0x80
disk=/dev/hda
bios=0x81

Every BIOS can use a different set of rules to assign drive IDs so watch out for problems when you change the order that drives are booted in the BIOS. It may cause unrelated drive IDs to change as well as the ones for the old and new "first disk drive" in the list. Plugging in a USB drive may change BIOS drive IDs if the BIOS has never detected a USB hard disk and added one into the list.

I find that a GRUB boot disk is useful because GRUB has a "find" command that will identify which drives contain a file.

find /boot/vmlinuz

When you boot GRUB from a CD or floppy into "native" command mode then it names disks based on BIOS drive IDs.

(hd0) - 80 hex
(hd1) - 81 hex
(hd2) - 82 hex
(hd3) - 83 hex

Partitions are named like this.

(hd?,0) First Primary partition (or extended)
(hd?,1) First Primary partition (or extended)
(hd?,2) First Primary partition (or extended)
(hd?,3) First Primary partition (or extended)
(hd?,4) First Logical partition inside Extended partition
(hd?,5) First Logical partition inside Extended partition

Replace the "?" with the number of the drive, 0, 1, 2, etc. For example, "(hd1,3)" for the second drive, fourth partition.

When you run GRUB from Linux it has to figure out the drive IDs from the device names just like LILO, and can get them wrong. There is a "map" file that you can create to tell GRUB the device to drive ID mapping. Booting into GRUB native command prompt without Linux avoids the problem since GRUB accesses all drives through the BIOS drive IDs and not Linux device names.

There are other ways to determine drive IDs, including using FREEDOS or some other OS that can call the BIOS directly.